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PeterColes

COSMOLOGYAVeryShortIntroduction

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Preface

This book is an introduction to the ideas, methods, and results of scientificcosmology.

Thesubjectmatterofcosmologyiseverythingthatexists.Theentiresystemofthings that is theUniverse encompasses thevery largeand thevery small, theastronomicalscaleofstarsandgalaxiesandthemicroscopicworldofelementaryparticles.Betweentheselimitsliesacomplexhierarchyofstructureandpatternthatresultsfromtheinterplayofforcesandmatter.Andinthemidstofallthiswefindourselves.

Theaimofcosmologyistoplaceallknownphysicalphenomenawithinasinglecoherent framework. This is an ambitious goal, and significant gaps in ourknowledge still remain. Nevertheless, there has been such rapid progress thatmanycosmologistsregardthisassomethingofa‘GoldenAge’.Ihavetakenaroughlyhistoricalpath through thesubject toshowhowithasevolved,howithasdrawn togethermanydifferent conceptual strands along theway, andhownewavenuesforexplorationhaveopenedupwithimprovementsintechnology.

It isagood time towrite thiskindofbook.Anemergingconsensusabout theform and distribution of matter and energy in the Universe suggests that acomplete understanding of it all may bewithin reach. But interesting puzzlesremain,andifhistorytellsusanythingitisthatweshouldexpectsurprises!

Contents

Listofillustrations

1Abriefhistory

2Einsteinandallthat

3Firstprinciples

4TheexpandingUniverse

5TheBigBang

6What’sthematterwiththeUniverse?

7Cosmicstructures

8Atheoryofeverything?

Epilogue

Furtherreading

Index

Listofillustrations

1TheBabylonianGodMardukFromTheMythologyofAllRaces, ed. J.A.MacCulloch (CooperSquare,1964);seeEchoesoftheAncientSkies,E.C.Krupp,p.68.

2Thought-experimentillustratingtheequivalenceprincipleFromP.Coles,EinsteinandtheBirthofBigScience(IconBooks,2000)

3ThebendingoflightFromP.Coles,EinsteinandtheBirthofBigScience(IconBooks,2000)

4ThecurvatureofspaceFromP.Coles,EinsteinandtheBirthofBigScience(IconBooks,2000)

5Open,flat,andclosedspacesintwodimensions

6Hubble’sLaw

7TheHubblediagramFromHubble(1929),ProceedingsofNat.Acad.Sci.,15,168–173;seeTheExpandingUniverse,R.C.Smith,p.92

8Redshift

9TheHubblediagramupdated

10TheHubbleSpaceTelescopeSpaceTelescopeScienceInstitute

11CepheidsinM100SpaceTelescopeScienceInstitute

12TheageoftheUniverse

13ThespectrumofthecosmicmicrowavebackgroundNASAandGeorgeSmoot

14Lookingbackintime

15BuildingblocksofmatterFermiNationalAcceleratorLaboratory

16TheFriedmannmodels

17TheComaclusterNationalOpticalAstronomyObservatories

18ComainX-raysHighEnergyAstrophysicsArchiveResearchCenter

19GravitationallensingSpaceTelescopeScienceInstitute

20TheAndromedaNebulaJasonWare

21TheLickMapSteveMaddox

22The2dFgalaxyredshiftsurveySteveMaddoxandthe2dFConsortium

23TheCOBEripplesNASAandGeorgeSmoot

24TheHubbledeepfieldTheVirgoConsortium

25SimulationofstructureformationSpaceTelescopeScienceInstitute

26BOOMERANG

TheBoomerangCollaboration

27TheflatnessofspaceTheBoomerangCollaboration

28Atheoryofeverything

29Space–timefoamFrom300YearsofGravity,ed.S.W.HawkingandW.Israel(CambridgeUniversityPress,1987),p.625

Chapter1Abriefhistory

Cosmology is a relatively new branch of physical science. This is quite aparadoxical state of affairs, because among the questions cosmology asks aresomeofthemostancientthathumanityhaseverposed.IstheUniverseinfinite?Has it been around for ever? If not, how did it come into being?Will it evercometoanend?Sinceprehistorictimes,humanshavesoughttobuildsomekindof conceptual framework for answering questions about the world and theirrelationshiptoit.Thefirstsuchtheoriesormodelsweremythsthatwenowadaysregardasnaiveormeaningless.ButtheseprimitivespeculationsdemonstratetheimportanceweasaspecieshavealwaysattachedtothinkingabouttheUniverse.Today’s cosmologists use very different language and symbolism, but theirmotivationislargelythesameasourdistantancestors.WhatIwanttodointhischapter is briefly chart the historical development of cosmology ‘the subject’and explain how some of the key ideas have evolved. I hope this will alsoprovideausefulspringboardintotheotherchaptersinwhichIexplorethesekeyideasinmoredetail.

TheUniverseinmyth

Most early cosmologies are based on some form of anthropomorphism (theinterpretation of something which is not human, in terms of humancharacteristics). Some involve the idea that the physicalworld is animated bywilful beings that can help or hindermankind, others that the physical worlditselfisinanimatebutcanbemanipulatedbyagodorgods.Eitherway,creationmyths tend to explain the origin of the Universe in terms of entities whosemotivescanbeunderstood,atleastpartly,byhumanbeings.

There aremany differences in creationmyths around theworld, but there arealso some striking similarities. For one thing, their imagery often incorporatesthe idea of a supreme craftsman. The beauty of the natural world is thusrepresentedasthehandiworkofaskilledartisan,examplesofwhicharefoundinall cultures. Another recurring image is the growth of order from chaos,mirroringtheprogressiveorganizationofhumansociety.YetanotherparallelistheUniverseasabiologicalprocess.Themoststrikingexamplesofthisoccurinmythsthatdepictthecosmosasformingfromaneggorseed.

TheBabylonianversionofGenesis, theEnumaElish, contains theseelements.Thismyth dates from around 1450BCE, but is probably based onmuch olderSumerianversions.Initsaccountofthecreation,theprimordialstateofdisorderis identifiedwith the sea. From the sea emerges a series of gods representingfundamental properties of theworld, such as the sky, the horizon, and so on.Twoof thesedeities,MardukandTiamat, fight andTiamat the sea-goddess iskilled.MardukmakestheEarthfromherbody.

Chinaalsofurnishesinterestingillustrations.OneinvolvesthegiantPanGu.Inthis story, the cosmosbeganas agiant egg.Thegiant slept inside the egg forthousands of years before he awoke and broke free, shattering the egg in theprocess.Somepartsof theegg (the lighterandpurerbits) roseup to form theheavenswhile theheavier, impureparts formed theEarth.PanGuheldup theheavenswithhishandswhilehisfeetrestedontheEarth.Astheheavensdriftedhigher, thegiantgrewtallertokeepthemincontactwiththeEarth.EventuallyPanGudied,buthisbodypartswereput togooduse.His lefteyebecametheSun,hisrighteyetheMoon.Hissweatbecametherain,hishairtheplantsoftheEarth,andhisbonestherocks.

1. The Babylonian God Marduk. Marduk is credited with the imposition ofcosmic order after the destruction of Tiamat, the embodiment of primordialchaos,shownhereathisfeetintheformofahorneddragon.Manymythologiesaroundtheworldincorporatetheideathatorderarosefromchaos,andthethemesurvivesinsomeaspectsofmodernscientificcosmology.

Thereareasmanycreation legendsas therehavebeencultures,andIhavenospace to give more examples here. Whether African, Asian, European, orAmerican,itisstrikinghowmanyformalsimilaritiesthesemythsdisplay.

TheGreeks

Western sciencehas its roots inGreece.TheGreeks,of course,had theirowngods and myths, many of them borrowed from neighbouring cultures. But

alongside thesemore traditional elements they began to establish a system ofprinciples for scientific enquiry.The identificationof cause and effect, still anessential component of scientific theories,was down to theGreeks.They alsorealized that descriptions and explanations of observed phenomena could bephrasedinmathematicalorgeometricalratherthananthropomorphicterms.

Cosmology began to emerge as a recognizable scientific disciplinewithin theoverall framework of rational thought constructed by the Greeks, notablythrough Thales (625–547 BCE) and Anaximander (610–540 BCE). The wordcosmologyitself isderivedfromtheGreek‘cosmos’,meaning theworldasanordered system or whole. The emphasis is just as much on order as onwholeness, for inGreektheoppositeof‘cosmos’ is‘chaos’.ThePythagoreansof the sixth century BCE regarded numbers and geometry as the basis of allnaturalthings.Theadventofmathematicalreasoning,andtheideathatonecanlearnabout thephysicalworldusinglogicandreasonmarkedthebeginningofthe scientific era. Plato (427–348 BCE) expounded a complete account of thecreation of theUniverse, inwhich a divineDemiurge creates, in the physicalworld,imperfectrepresentationsofthestructuresofpurebeingthatexistonlyintheworldofideas.Thephysicalworldissubjecttochange,whereastheworldofideasiseternalandimmutable.

Aristotle(384–322BCE),apupilofPlato,builtontheseideastopresentapictureof the world in which the distant stars and planets execute perfect circularmotions,circlesbeingamanifestationof‘divine’geometry.Aristotle’sUniverseisaspherecentredontheEarth.ThepartofthisspherethatextendsasfarastheMoonisthedomainofchange,theimperfectrealityofPlato,butbeyondthistheheavenly bodies execute their idealized circular motions. This view of theUniverse was to dominate Western European thought throughout the MiddleAges, but its perfect circularmotions did notmatch the growing quantities ofastronomicaldatabeinggatheredbytheGreeksfromtheastronomicalarchivesmadebytheBabyloniansandEgyptians.AlthoughAristotlehademphasizedthepossibilityoflearningabouttheUniversebyobservationaswellaspurethought,itwasnotuntilPtolemy’sAlmagest, compiled in thesecondcenturyCE, thatacompletemathematicalmodelfortheUniversewasassembledthatagreedwithallthedataavailable.

TheRenaissance

Much of the knowledge acquired by the Greeks was lost to Christian cultureduring the dark ages, but it survived in the Islamic world. As a result,cosmological thinkingduring theMiddleAgesofEuropewasrather restricted.ThomasAquinas(1225–74)seizedonAristotle’sideas,whichwereavailableinLatintranslationatthetimewhiletheAlmagestwasnot,toforgeasynthesisofpagan cosmology with Christian theology which was to dominate Westernthoughtuntilthesixteenthandseventeenthcenturies.

Thedismantlingof theAristotelianworld-view is usually credited toNicolausCopernicus (1473–1543). Ptolemy’s Almagest was a complete theory, but itinvolved applying a different mathematical formula for the motion of eachplanet and therefore did not really represent an overall unifying system. In asense,itdescribedthephenomenaofheavenlymotionbutdidnotexplainthem.Copernicuswantedtoderiveasingleuniversaltheorythattreatedeverythingonthesamefooting.Heachievedthisonlypartially,butdidsucceedindisplacingthe Earth from the centre of the scheme of things. It was not until JohannesKepler(1571–1630)camealongthatacompletelysuccessfuldemolitionof theAristotelian system was achieved. Driven by the need to explain the highlyaccurateobservationsofplanetarymotionmadebyTychoBrahe (1546–1601),KeplerreplacedAristotle’sdivinecircularorbitswithellipses.

Thenextgreatdevelopmenton the road tomoderncosmological thinkingwasthe arrival on the scene of Isaac Newton (1642–1727). Newton was able toshow,inhismonumentalPrincipia(1687),thattheellipticalmotionsdevisedbyKepler were the natural outcome of a universal law of gravitation. Newtonthereforere-establishedakindofPlatoniclevelofreality,theidealizedworldofuniversallawsofmotion.TheUniverse,inNewton’spicture,behavesasagiantmachine,enactingtheregularmotionsdemandedbythedivineCreatorandbothtimeandspaceareabsolutemanifestationsofaninternalandomnipresentGod.

Newton’sideasdominatedscientificthinkinguntilthebeginningofthetwentiethcentury, but by the nineteenth century the cosmic machine had developedimperfections. The mechanistic world-view had emerged alongside the firststirrings of technology.During the subsequent IndustrialRevolution, scientistshad become preoccupied with the theory of engines and heat. These laws ofthermodynamicshadshownthatnoenginecouldworkperfectlyforeverwithoutrunningdown.Inthistimetherearoseawidespreadbeliefinthe‘HeatDeathoftheUniverse’, the idea that thecosmosasawholewouldeventually fizzleoutjustasabouncingballgraduallydissipatesitsenergyandcomestorest.

Towardsthemodernera

Another spanner was thrown into the works of Newton’s cosmic engine byOlbers(1758–1840),whoformulatedin1826aparadoxthatstillbearshisnamealthough it was discussed by many before him, including Kepler. Olbers’Paradoxemergesfromconsideringwhythenightskyisdark.InaninfiniteandunchangingUniverse,every lineofsight fromanobservershouldhitastar, inmuchthesamewayasalineofsightthroughaninfiniteforestwilleventuallyhita tree. The consequence of this is that the night sky should be as bright as atypical star.Theobserveddarknessatnight is sufficient toprove theUniversecannotbebothinfiniteandeternal.

Whether the Universe is infinite or not, the part of it accessible to rationalexplanation has steadily increased. For Aristotle, the Moon’s orbit (a mere400,000 km) marked a fundamental barrier, beyond which the human mindcouldnotreach.ToCopernicusandKepler the limitwas theedgeof theSolarSystem (billions of kilometres away). By the eighteenth and nineteenthcenturies,itwasbeingsuggestedthattheMilkyWay,astructurenowknowntobeatleastabilliontimeslargerthantheSolarSystem,wastheentireUniverse.This suggestion had a rival, the idea that many strange spiral ‘nebulae’discoveredscatteredacrosstheskywereobjectsverysimilartoourMilkyWaybutseenatimmensedistances.Theseobjectswouldcometobecalledgalaxies.A‘GreatDebate’tookplaceintheearlyyearsofthetwentiethcenturybetweenthese twoopposing ideas,whichIwilldiscuss inChapter4.Thanks largely toEdwinHubble(1889–1953),itisnowknownthattheMilkyWayisindeedonlyoneofhundredsofbillionsofsimilargalaxies.

Themoderneraofcosmologybeganintheearlyyearsofthetwentiethcentury,with a complete rewrite of the laws of nature. Albert Einstein (1879–1955)introducedtheprincipleofrelativityin1905andtherebydemolishedNewton’sconception of space and time. Later, his general theory of relativity alsosupplanted Newton’s law of universal gravitation. The first great works onrelativistic cosmology byFriedmann (1888–1925),Lemaître (1894–1966), andde Sitter (1872–1934) formulated a new and complex language for themathematical description of the Universe. Einstein’s theory plays such afundamentalconceptualroleinmoderncosmologythatIwilldevotemuchofthenextchaptertoit.

Butwhiletheseconceptualdevelopmentspavedtheway,thefinalstepstowardsthemodern era were taken not by theoretical physicists, but by observationalastronomers. In 1929, Edwin Hubble, who had only recently shown that theUniverse contained many galaxies like the Milky Way, published theobservationsthatledtotherealizationthatourUniverseisexpanding.Finally,in1965,PenziasandWilsondiscoveredthecosmicmicrowavebackground,proof(or as near to proof as you’re likely to see) that our Universe began in aprimordialfireball–theBigBang.

Cosmologytoday

ThemoderneraofscientificcosmologybeganwithEinstein’sgeneraltheoryofrelativity, published in 1915, which made possible a consistent mathematicaldescriptionoftheentireUniverse.AccordingtoEinstein’stheory,thepropertiesof matter and motion are related to deformations of space and time. Theimportanceofthisforcosmologyisthatspaceandtimearenolongerthoughtofas absolute and independent of material bodies, but as participants in theevolution of the Universe. General relativity allows us to understand not theorigin of the cosmos in space and time, but the origin of space and timethemselves.

Einstein’s theory forms the basis of the modern Big Bang model, which hasemergedasthebestavailabledescriptionoftheexpandingUniverse.Accordingto this model, space, time, matter, and energy all came into existence as aprimordial fireball of matter and radiation at extremes of temperature anddensity about 15 billion years ago. A few seconds after the beginning, thetemperature had decreased to amere 10 billion degrees and nuclear reactionsbegantomaketheatomsfromwhichweareallmade.Afterabout300,000yearsthetemperaturehadfallentoafewthousanddegrees,releasingtheradiationwenowobserveasthecosmicmicrowavebackground.Asthisexplosionexpanded,carrying space and time with it, the Universe cooled and rarefied. Stars andgalaxiesformedbycondensingoutoftheexpandingcloudofgasandradiation.Ourpresent-dayUniversecontains theashesandsmoke leftover fromtheBigBang.

Chapter 5 describes the Big Bang theory in more detail. Most cosmologistsaccept it as being essentially correct, as far as it goes. It explainsmost of the

thingsweknowabout thebulkpropertiesof theUniverse,andcanaccountformost relevantcosmologicalobservations.But it is important to realize that theBigBangisnotcomplete.Muchofmoderncosmologicalresearchisdrivenbythedesiretofillthegapsinthisotherwisecompellingframework.

Foronething,Einstein’stheoryitselfbreaksdownattheverybeginningoftheUniverse. The Big Bang is an example of what relativity theorists call asingularity, a point where the mathematics falls to pieces and measurablequantities become infinite. While we know how the Universe is expected toevolvefromagivenstage,thesingularitymakesitimpossibletoknowfromfirstprinciples what the Universe should look like in the beginning.We thereforehave to piece this together using observations rather than pure thought, likearchaeologiststryingtoreconstructacityfromruins.Modern-daycosmologistsare therefore collectinghugequantities of detaileddata so that they can try topieceitalltogethertomakeapictureofhowtheUniversebegan.

Technological developments over the last twenty years have acceleratedprogressinobservationalcosmologytoaremarkableextent,andwearetrulyina‘GoldenAge’ofcosmicdiscovery.Observationalcosmologynowincludestheconstructionofhugemapsofthedistributionofgalaxiesinspace,showingtheremarkable large-scale structure of filaments and sheets. These surveys arecomplementedbydeepobservationsbeingmadewith,forexample,theHubbleSpaceTelescope.TheHubbleDeepFieldissuchalongexposurethatitcanseegalaxies at distances so huge that it has taken light much of the age of theUniversetoreachusfromthem.Usingobservationslikethiswecanseecosmichistoryunfolding.For example,microwaveastronomers arenowable tomakepicturesofthestructureoftheearlyUniversebyobservingripplesinthecosmicmicrowave background produced in the primordial fireball. Planned satelliteexperiments,suchasMAPandthePlanckSurveyor,willprobetheseripplesinmore detail over the next few years and the results they produce should plugmanyofthegapsinourunderstandingofhowtheUniverseisputtogether.

Astronomicalobservationscanbeusedtomeasuretherateofcosmicexpansion,how this is changing with time, and also to probe the geometry of space byapplying the principles of triangulation on an enormous scale. In Einstein’stheory,lightraysdonotnecessarilytravelinstraightlinesbecausespacedistortsin response to the gravity produced by massive bodies. Over cosmologicaldistances, thiseffectcanclose thewholeof space-timebackon itself (like thesurfaceofasphere)causingthepathsofparallellightraystoconverge.Itcould

alsoproducean‘open’Universeinwhichlightraysdiverge.Poisedinbetweenthesetwoalternativesisthe‘normal’ideaofflatspaceinwhichEuclid’slawsofgeometry apply.Which of these alternatives is correct depends upon the totalcosmic density ofmatter and energy,which theBigBang theory cannot itselfpredict.

TheBigBangtheoryunderwentamajortheoreticaloverhaulintheearly1980s,whenparticlephysiciststookupcosmologyasawayoftryingtounderstandtheproperties of matter at the extremely high energies their particle acceleratorscouldn’t reach. These theorists realized that the early Universe would beexpected to undergo a series of dramatic transformations known as phasetransitions,duringwhichitsexpansionwouldacceleratebyanenormousfactorinatinyfractionofasecond.Suchaperiodof‘inflation’isexpectedtoflattenout the curvature of space leading to a definite prediction that the Universeshouldbe flat.Thisseems tobeconsistentwith thecosmicsurveysmentionedabove. Recent suggestions that the expansion of the Universe may beacceleratingevennow,suggesttheexistenceofamysteriousdarkenergythatisperhapssomerelicoftheearlierinflationaryphase.

Cosmologistshavealsoappliedmodernsupercomputerstothebusinessoftryingto understand the condensation of clumps of cosmic material into stars andgalaxiesas theUniverseexpandsandcools.Thesecalculationshavesuggestedthatthisprocessrequirestheexistenceofhugeconcentrationsofexoticmaterial,denseenoughtoassist thegrowthofstructure,yetproducingnostarlight.Thisinvisible stuff is called dark matter. Computer predictions of the structureformedareincloseagreementwiththehugemapsbeingmadebytheobserverslendingfurthersupporttotheBigBangtheory.

The interplay between these new theoretical ideas and new high-qualityobservationaldatahascatapultedcosmologyfromthepurelytheoreticaldomainand into the field of rigorous experimental science. This process began at thebeginningofthetwentiethcentury,withtheworkofAlbertEinstein.

Chapter2Einsteinandallthat

Weareall awareof theeffectsofgravity.Objects fall toEarthwhenwedropthem.It’shardertorunuphillthandown.Toaphysicist,however,thereismuchmoretogravitythanitseffectsonoureverydaylives.Foronething,thelargerthe scale of things being considered, the more important gravity becomes.Gravitypulls theEartharoundtheSun,and theMoonaroundtheEarth,and itcauses tides.Onthescaleof thingsrelevant toastronomy,gravity is theprimemover. So if you want to understand the Universe as a whole, you have tounderstandgravity.

Universalgravitation

Gravity is one of the fundamental forces of nature. It represents the universaltendency of all matter to attract all other matter. There are in fact fourfundamental forces (gravity, electromagnetism, and the ‘weak’ and ‘strong’nuclear forces).Theuniversalityofgravity sets it apart from, forexample, theelectrical forces between charged bodies. Electrical charges can be of twodifferent kinds, positive or negative.While electrical forces can lead either toattraction(betweenunlikecharges)orrepulsion(betweenlikecharges),gravityisalwaysattractive.Thatiswhyitissoimportantforcosmology.

Inmanyways,theforceofgravityisextremelyweak.Mostmaterialbodiesareheld together by electrical forces between atoms which are many orders ofmagnitudestronger than thegravitational forcesbetween them.But,despite itsweakness, gravity is the driving force in astronomical situations becauseastronomicalbodies,withveryfewexceptions,alwayscontainexactlythesame

amount of positive andnegative charge and therefore never exert forces of anelectricalnatureoneachother.

One of the first great achievements of theoretical physicswas IsaacNewton’stheory of universal gravitation,which unifiedwhat, at the time, seemed to bemanydisparatephysicalphenomena.Newton’stheoryofmechanicsisencodedinthreesimplelaws:

1.Everybodycontinues ina stateof restoruniformmotion ina straightlineunlessitiscompelledtochangethatstatebyforcesimpresseduponit.

2.Rateofchangeofmomentumisproportionaltotheimpressedforce,andisinthedirectioninwhichthisforceacts.

3.Toeveryaction,thereisalwaysopposedanequalreaction.

These three laws of motion are general, applying just as accurately to thebehaviourofballsonabilliardtableastothemotionoftheheavenlybodies.AllthatNewtonneededtodowastofigureouthowtodescribetheforceofgravity.Newtonrealizedthatabodyorbitinginacircle,liketheMoongoingaroundtheEarth,isexperiencingaforceinthedirectionofthecentreofmotion(justasaweighttiedtotheendofapieceofstringdoeswhenit istwirledaroundone’shead).Gravitycouldcausethismotioninthesamewayasitcouldcauseapplestofall toEarthfromtrees.Inboththesesituations, theforcehas tobetowardsthe centre of the Earth. Newton realized that the right form of mathematicalequation was an ‘inverse-square’ law: ‘the attractive force between any twobodiesdependsontheproductofthemassesofthebodiesanduponthesquareofthedistancebetweenthem.’

It was a triumph of Newton’s theory, based on the inverse-square law ofuniversalgravitation,thatitcouldexplainthelawsofplanetarymotionobtainedbyJohannesKeplermorethanacenturyearlier.SospectacularwasthissuccessthattheideaofaUniverseguidedbyNewton’slawsofmotionwastodominatescientificthinkingformorethantwocenturies,untilthearrivalonthesceneofAlbertEinstein.

TheEinsteinrevolution

AlbertEinsteinwasborninUlm(Germany)on14March1879,buthisfamilysoonmoved toMunich,where he spent his school years. The young Einsteinwas not a particularly good student, and in 1894 he dropped out of schoolentirelywhenhisfamilymovedtoItaly.Afterfailingtheentranceexaminationonce,hewaseventuallyadmittedtotheSwissInstituteofTechnologyinZurichin1896.AlthoughhedidfairlywellasastudentinZurich,hewasunabletogeta job in any Swiss university, as he was held to be extremely lazy. He leftacademia towork in thePatentOfficeatBern in1902.Thisgavehimagoodwageand,sincethetasksgiventoajuniorpatentclerkwerenotexactlyonerous,italsogavehimplentyofsparetimetothinkaboutphysics.

Einstein’sspecialtheoryofrelativitywaspublishedin1905.Itstandsasoneofthegreatestintellectualachievementsinthehistoryofhumanthought.Itismadeevenmore remarkable by the fact that Einstein was still working as a patentclerk at the time, and was doing physics as a particularly demanding hobby.What’s more, he also published seminal works that year on the photoelectriceffect(whichwastoinspiremanydevelopmentsinquantumtheory)andonthephenomenonofBrownianmotion(thejigglingofmicroscopicparticlesas theyare buffeted by atomic collisions). But the reason why the special theory ofrelativitystandsheadandshouldersabovehisownworkofthistime,andthatofhiscolleagues in theworldofmainstreamphysics, is thatEinsteinmanaged tobreak away completely from the concept of time as an absolute property thatmarchesonatthesamerateforeveryoneandeverything.Thisideaisbuiltintothe Newtonian picture of the world, and most of us regard it as being soobviouslytruethat itdoesnotbeardiscussion.It takesageniustobreakdownconceptualbarriersofsuchmagnitude.

TheideaofrelativitydidnotoriginatewithEinstein.Galileohadarticulatedthebasicprinciplenearly threecenturiesearlier.Galileoclaimed thatonly relativemotionmatters,sotherecouldbenosuchthingasabsolutemotion.Hearguedthat if youwere travelling in a boat at constant speed on a smooth lake, thentherewouldbenoexperimentthatyoucoulddoinasealedcabinontheboatthatwould indicate to you that youweremoving at all. Of course, notmuchwasknown about physics in Galileo’s time, so the kinds of experiment he couldenvisagewereratherlimited.

Einstein’sversionoftheprincipleofrelativitysimplyturneditintothestatementthatall lawsofnaturehave tobeexactly thesameforallobservers in relativemotion. In particular, Einstein decided that this principle must apply to the

theory of electromagnetism, constructed by James Clerk Maxwell, whichdescribes amongst other things the forces between charged bodies mentionedabove.OneoftheconsequencesofMaxwell’stheoryisthatthespeedoflight(invacuum)appearsasauniversalconstant(usuallygiventhesymbol‘c’).Takingtheprincipleofrelativityseriouslymeansthatallobservershavetomeasurethesame value of c, whatever their state of motion. This seems straightforwardenough,buttheconsequencesarenothingshortofrevolutionary.

Einsteindecidedtoaskhimselfspecificquestionsaboutwhatwouldbeobservedin particular kinds of experiments involving the exchange of light signals.Heworked a great deal with gedanken (thought) experiments of this kind. Forexample,imaginethereisaflashbulbinthecentreofarailwaycarriagemovingalongatrack.Ateachendofthecarriagethereisaclock,sothatwhentheflashilluminates it we can see the time. If the flash goes off, then the light signalreaches both ends of the carriage simultaneously, from the point of view ofpassengerssittinginthecarriage.Thesametimeisseenoneachclock.

Nowpicturewhathappensfromthepointofviewofanobserveratrestwhoiswatchingthetrainfromthetrack.Thelightflashtravelswiththesamespeedinourreferenceframeasitdidforthepassengers.Butthepassengersatthebackofthecarriagearemovingintothesignal,whilethoseatthefrontaremovingawayfromit.Thisobserver thereforesees theclockat thebackof the train lightupbeforetheclockatthefrontdoes.Butwhentheclockatthefrontdoeslightup,itreadsthesametimeastheclockatthebackdid!Thisobserverhastoconcludethatsomethingiswrongwiththeclocksonthetrain.

This example demonstrates that the concept of simultaneity is relative. Thearrivalsofthetwolightflashesaresimultaneousintheframeofthecarriage,butoccur at different times in the frame of the track. Other examples of strangerelativisticphenomenaincludetimedilation(movingclocksappeartorunslow)and length contraction (moving rulers appear shorter). These are allconsequences of the assumption that the speed of light must be the same asmeasured by all observers. Of course, the examples given above are a littleunrealistic.Inordertoshownoticeableeffects,thevelocitiesconcernedmustbea sizeable fraction of c. Such speeds are unlikely to be reached in railwaycarriages.Nevertheless,experimentshavebeendonethatshowthattimedilationeffectsarereal.Thedecayrateofradioactiveparticlesismuchslowerwhentheyaremovingathighvelocitiesbecausetheirinternalclockrunsslowly.

Specialrelativityalsospawnedthemostfamousequationinallofphysics:E=mc2,expressingtheequivalencebetweenmatterandenergy.Thishasalsobeentestedexperimentally;amongstotherthingsitistheprinciplebehindbothatomicandchemicalexplosives.

Remarkablethoughthespecialtheoryundoubtedlyis,itisseriouslyincompletebecauseitdealsonlywithbodiesmovingwithconstantvelocitywithrespecttoeachother.Evenchapter1of the lawsofnature,writtenbyNewton,hadbeenbuilt around the causes and consequences of velocities that changewith time.Newton’s second law is about the rate of change ofmomentum of an object,whichinlayman’stermsisitsacceleration.Specialrelativityisrestrictedtoso-called inertialmotions, i.e. themotionsofparticles that arenot acteduponbyany external forces. This means that special relativity cannot describeacceleratedmotionofanykindand,inparticular,cannotdescribemotionundertheinfluenceofgravity.

Theequivalenceprinciple

Einstein had deep insights into how to incorporate gravitation into relativitytheory.Forastart,considerNewton’stheoryofgravity.Inthistheory,theforceonaparticleofmassmduetoanotherparticleofmassMdependsontheproductofthesemassesandthesquareofthedistancebetweentheparticles.Accordingto Newton’s laws of motion, this induces an acceleration in the first particlegivenbyF=ma.Theminthisequationiscalledtheinertialmassoftheparticle,and it determines the particle’s resistance to being accelerated. In the inverse-squarelawofgravity,however,themassmmeasuresthereactionofoneparticletothegravitationalforceproducedbytheotherparticle.Itisthereforecalledthepassivegravitationalmass.ButNewton’sthirdlawofmotionalsostatesthatifbodyAexertsaforceonbodyBthenbodyBexertsaforceonbodyAwhichisequalandopposite.Thismeansthatmmustalsobetheactivegravitationalmass(if you like, the gravitational charge) produced by the particle. In Newton’stheory, all three of these masses – the inertial mass, the active and passivegravitationalmasses– are equivalent.But there seems tobeno reason,on thefaceofit,whythisshouldbethecase.Couldn’ttheybedifferent?

Einstein decided that this equivalence must be the consequence of a deeperprinciplecalledtheprincipleofequivalence.Inhisownwords,thismeansthat

‘all local, freely-falling laboratories are equivalent for the performance of allphysicalexperiments’.Whatthismeansisessentiallythatonecandoawaywithgravity as a separate forceofnature and regard it insteadas a consequenceofmovingbetweenacceleratedframesofreference.

Toseehowthisispossible,imaginealiftequippedwithaphysicslaboratory.Ifthe lift is at rest on the ground floor, experimentswill reveal the presence ofgravity to theoccupants.Forexample, ifweattachaweightonaspringto theceilingof the lift, theweightwillextend thespringdownwards.Next, imaginethatwetakethelifttothetopofabuildingandletitfallfreely.Insidethefreelyfalling lift there is no perceptible gravity. The spring does not extend, as theweightisalwaysfallingat thesamerateastherestofthelift,eventhoughthelift’sspeedmightbechanging.Thisiswhatwouldhappenifwetooktheliftoutinto space, far away from the gravitational field of the Earth. The absence ofgravity therefore looks very much like the state of free-fall in response to agravitational force.Moreover, imagine that our liftwas actually in space (andout of gravity’s reach), but therewas a rocket attached to it. Firing the rocketwouldmaketheliftaccelerate.Thereisnoupordowninfreespace,butletusassumethattherocketisattachedsothattheliftwouldaccelerateintheoppositedirectionfrombefore,i.e.inthedirectionoftheceiling.

What happens to the spring? The answer is that the acceleration makes theweightmoveinthereversedirectionrelativetothelift,thusextendingthespringtowardsthefloor.(Thisislikewhathappenswhenacarsuddenlyaccelerates–the passenger’s head is flung backwards.) But this is just likewhat happenedwhentherewasagravitationalfieldpullingthespringdown.Iftheliftcarriedonaccelerating,thespringwouldremainextended,justasifitwerenotacceleratingbutplacedinagravitationalfield.Einstein’sideawasthatthesesituationsdonotmerely appear similar: they are completely indistinguishable. Any experimentperformedinanacceleratedliftinspacewouldgiveexactlythesameresultsasoneperformed in a lift uponwhichgravity is acting.To complete thepicture,nowconsideraliftplacedinsidearegion

2. Thought-experiment illustrating the equivalence principle. A weight isattached to a spring,which is attached to the ceilingof a lift. In (a) the lift isstationary,but agravitational force actsdownwards; the spring is extendedbytheweight.In(b)theliftisindeepspace,awayfromanysourcesofgravity,andis not accelerated; the spring does not extend. In (c) there is no gravitationalfield,buttheliftisacceleratedupwardsbyarocket;thespringisextended.Theaccelerationin(c)produces thesameeffectas thegravitationalforcein(a). In(d)theliftisfreelyfallinginagravitationalfield,acceleratingdownwardssonogravityisfeltinside;thespringdoesnotextendbecauseinthiscasetheweightisweightlessandthesituationisequivalentto(b).

wheregravity is acting, butwhich is allowed to fall freely in thegravitationalfield.Everythinginsidebecomesweightless,andthespringisnotextended.Thisisequivalenttothesituationinwhichtheliftisatrestandwherenogravitationalforcesareacting.Afreelyfallingobserverhaseveryreasontoconsiderhimselftobeinastateofinertialmotion.

Thegeneraltheoryofrelativity

Einsteinnowknewhowheshouldconstructthegeneraltheoryofrelativity.Butitwouldtakehimanothertenyearstoproducethetheoryinitsfinalform.Whathe had to findwas a set of laws that could dealwith any formof acceleratedmotion and any form of gravitational effect. To do this he had to learn aboutsophisticatedmathematical techniques,suchas tensoranalysisandRiemanniangeometry,andtoinventaformalismthatwastrulygeneralenoughtodescribeallpossible states of motion. He got there, but clearly it wasn’t easy.While hisclassic papers of 1905 were characterized by brilliant clarity of thought andeconomy of mathematical calculation, his later work is mired in technicaldifficulty.PeoplehavearguedthatEinsteingrewupasascientistwhilehewasdevelopingthegeneraltheory.Ifso,itwasobviouslyadifficultprocessforhim.

Understanding the technicalities of the general theory of relativity is a trulydaunting task.Evenonaconceptual level, the theory isdifficult tograsp.Therelativityoftimeembodiedinthespecialtheoryispresentinthegeneraltheory,but there are additional effects of time dilation and length contraction due togravitational effects. And the problems don’t end with time! In the specialtheory,spaceatleastiswellbehaved.Inthegeneraltheory,eventhisgoesoutofthewindow.Spaceiscurved.

Thecurvatureofspace

Theideathatspacecouldbewarpedissodifficulttograspthatevenphysicistsdon’treally try tovisualizesucha thing.Ourunderstandingof thegeometricalpropertiesof thenaturalworld is basedon the achievementsof generationsofGreekmathematicians, notably the formalized system ofEuclid – Pythagoras’theorem,parallellinesnevermeeting,thesumoftheanglesofatriangleaddingupto180degrees,andsoon.AlloftheserulesfindtheirplaceinthecanonofEuclidean geometry. But these laws and theorems are not just abstractmathematics. We know from everyday experience that they describe theproperties of the physicalworld extremelywell. Euclid’s laws are used everydaybyarchitects,surveyors,designers,andcartographers–anyone,infact,whoisconcernedwiththepropertiesofshape,andthepositioningofobjectsinspace.Geometryisreal.

It seems self-evident, therefore, that these properties of space that we havegrownupwithshouldapplybeyondtheconfinesofourbuildingsandthelandswesurvey.TheyshouldapplytotheUniverseasawhole.Euclid’slawsmustbebuilt into the fabric of the world. Or must they? Although Euclid’s laws aremathematically elegant and logically compelling, they are not the only set ofrules that can be used to build a system of geometry.Mathematicians of thenineteenth century, such as Gauss and Riemann, realized that Euclid’s lawsrepresent only a special case of geometry wherein space is flat. Differentsystemscanbeconstructedinwhichtheselawsareviolated.

Consider, for example, a triangle drawn on a flat sheet of paper. Euclid’stheoremsapplyhere, so thesumof the internalanglesof this trianglemustbe180degrees(equivalenttotworight-angles).Butnowthinkaboutwhathappensifyoudrawatriangleonasphereinstead.Itisquitepossibletodrawatriangleonaspherethathasthreerightanglesinit.Forexample,drawonepointatthe‘north pole’ and two on the ‘equator’ separated by one quarter of thecircumference. These three points form a triangle with three right angles thatviolatesEuclideangeometry.

Thinkingthiswayworksfinefortwo-dimensionalgeometry,butourworldhasthree dimensions of space. Imagining a three-dimensional curved surface ismuchmoredifficult.Butinanycaseitisprobablyamistaketothinkof‘space’at all.After all,onecan’tmeasure space.Whatonecanmeasurearedistancesbetween objects located in space using rulers or, more realistically in anastronomicalcontext,lightbeams.Thinkingofspaceasaflatorcurvedpieceofpaperencouragesonetothinkofitasatangiblethinginitself,ratherthansimplyaswherethetangiblethingsarenot.Einsteinalwaystriedtoavoiddealingwithentitiessuchas‘space’whosecategoryofexistencewasunclear.Hepreferredtoreason insteadaboutwhatanobservercouldactuallyexpect tomeasurewithagivenexperiment.

Followingthislead,wecanaskwhatkindofpathlightraysfollowaccordingtothegeneral theoryofrelativity.InEuclideangeometry, light travelsonstraightlines.Wecan take the straightnessof lightpaths tomeanessentially the samethingas theflatnessofspace.Inspecialrelativity, lightalso travelsonstraightlines,sospaceisflatinthisviewoftheworldtoo.Butrememberthatthegeneraltheoryappliestoacceleratedmotion,ormotioninthepresenceofgravitationaleffects.Whathappenstolightinthiscase?

Letusgobacktothethoughtexperimentinvolvingthelift.Insteadofaspringwithaweightontheend,theliftisnowequippedwithalaserbeamthatshinesfromsidetoside.Theliftisindeepspace,farfromanysourcesofgravity.Ifthelift isstationary,ormovingwithconstantvelocity, thenthelightbeamhits thesideof the liftexactlyopposite to the laserdevice thatproduces it.This is theprediction of the special theory of relativity. But now imagine the lift has arocketwhichswitchesonandacceleratesitupwards.Anobserveroutsidetheliftwhoisatrest

3.Thebendingof light. In(a),our lift isacceleratingupwards,as inFig.2(c).Viewedfromoutside,alaserbeamfollowsastraightline.In(b),viewedinsidethelift,thelightbeamappearstocurvedownwards.Theeffectinastationaryliftsituatedinagravitationalfieldisthesame,asweseein(c).

seestheliftaccelerateaway,but ifhecouldseethelaserbeamfromoutsideitwould still be straight. On the other hand, a physicist inside the lift notices

somethingstrange.Intheshorttimeittakeslighttotravelfromonesideofthelifttotheother,thelift’sstateofmotionhaschanged.Ithasacceleratedsoitismovingfasterwhenthelightendsitsjourneythanitwaswhenthelightstartedout. This means that the point at which the laser beam hits the other wall isslightlybelow the startingpointon theother side.Seenbyanobserver inside,accelerationhas‘bent’thelightraydownwards.

Now remember the case of the spring and the equivalence principle. Whathappenswhen there is no accelerationbut there is a gravitational field is verysimilar to the accelerated lift. Consider now a lift standing on the Earth’ssurface.Thelightraymustdomuchthesamethingasintheacceleratinglift:itbendsdownward.Theconclusionweareledtoisthatgravitybendslight.Andiflightpathsarenotstraightbutbent,thenspaceisnotflatbutcurved.

One of the reasonswe find curved space hard to understand is that we don’tobserveit ineverydaylife.Thisisbecausegravityissoweakincommonplacecircumstances.EvenonthescaleofourSolarSystem,gravityissoweakthatthecurvature it causes is negligible and light travels in lines that are so nearlystraight thatwe can’t tell the difference. In these situations,Newton’s lawsofmotion are very good approximations to what happens. There are cases,however, where wemust be prepared to deal with strong gravity and all thatimplies.

BlackholesandtheUniverse

OneexamplewhereNewton’sgravitybreaksdowniswhenaverylargeamountofmatterisconcentratedinaverysmallregionofspace.Whenthishappenstheactionofgravityissostrong,andspacesowarped,thatlightisnotmerelybentbutistrapped.Suchanobjectisablackhole.

4.Thecurvatureofspace.Intheabsenceofasourceofgravitation,lighttravelsinastraightline.Ifamassiveobjectisplacednearthelightpath,thedistortionofspaceproducesabentlightray.

The idea thatblackholesmight exist innaturedatesback to JohnMichell, anEnglish clergyman, in 1783, andwas also discussed byLaplace. Such objectsare, however, most commonly associated with Einstein’s theory of generalrelativity.Indeed,oneofthefirstmathematicalsolutionsofEinstein’sequationsobtained, describes such an object. The famous ‘Schwarzschild’ solution wasobtainedonlyayearafter thepublicationofEinstein’s theory in1916byKarlSchwarzschild,whodiedsoonafterontheeasternfrontintheFirstWorldWar.Thesolutioncorrespondstoasphericallysymmetricdistributionofmatter,anditwasoriginally intendedthat thiscouldformthebasisofamathematicalmodelfor a star. It was soon realized, however, that for an object of any mass theSchwarzschildsolutionimpliedtheexistenceofacriticalradius(nowcalledtheSchwarzschildradius).IfamassiveobjectliesentirelywithinitsSchwarzschildradius thenno lightcanescapefromthesurfaceof theobject.For themassof

theEarththecriticalradiusisonly1cm,whereasfortheSunitisabout3km.Makingblackholesinvolvescompressingmaterialtoaphenomenaldensity.

Since thepioneeringworkofSchwarzschild, researchonblackholeshasbeenintense. Although there is as yet no truly watertight direct evidence for theexistenceofblackholesinnature,thereisamountainofcircumstantialevidencesuggesting they might be lurking in many kinds of astronomical object. Theintensegravitational field surroundingablackholeof about100million timesthe mass of the Sun is thought to be the engine that drives the enormousluminosityofcertaintypesofgalaxies.Morerecentobservationalstudiesofthedynamics of stars near the centre of galaxies indicate very strong massconcentrationsthatareusuallyidentifiedwithblackholeswithmassessimilartothis figure. It isnowthought tobeaseriouspossibility thatnearlyallgalaxieshave a black hole in their core. Black holes of much smaller mass may beformed at the end of the life of a star, when its energy source fails and itcollapsesinonitself.

Thereisagreatdealofinterestnowadaysinblackholes,buttheyarenotcentraltothedevelopmentofcosmologysoIshallnotdiscussthemfurtherinthisbook.Instead, in thenextchapterI’lldiscuss theroleEinstein’s theoryhasplayedinunderstandingthebehaviouroftheUniverseasawhole.

Chapter3Firstprinciples

Einsteinpublishedhisgeneraltheoryofrelativityin1915.Almostimmediatelyhe sought to exploit this new theoretical framework to explain the large-scalebehaviourof theentirecosmos.Hewashandicappedinhispursuitof thisgoalby the lack of information available to him about what it was that he wasattemptingtoexplain.WhatwastheUniversereallylike?Einstein’sknowledgeof astronomy was scanty, but he needed to know the answers to somefundamentalquestionsbeforehecouldproceed.HeknewthatpurethoughtalonecouldnottellhimwhattheUniverseshouldlooklikeandhowitshouldbehave.Observationsandguessworkwouldhavetoguidehim.

Simplicityandsymmetry

There is no doubt that the general theory furnishes an elegant conceptualframework, as I have tried to explain using thought experiments and pictures.The harsh truth, however, is that it involves some of the most difficultmathematics ever applied to a descriptionof nature.Togive some ideaof thecomplexity involved, it is useful to compare Einstein’s theory with the olderNewtonianapproach.

InNewton’s theory ofmotion there is basically onemathematical equation tosolve.Thisequation is ‘F=ma’,and it relates the forceFonanobject to theaccelerationaof thatobject. Itsoundssimpleenough,but inpractice itcanbeoverwhelminglycomplicatedtodescribegravityusingthisapproach.ThereasonisthateverypieceofmatterintheUniverseexertsagravitationalforceoneveryother. It’s relatively easy to apply this idea to the motion of two interacting

bodies,suchastheEarthandtheSun,butifyoustart toaddmorebodiesthenthingsgetverysticky.Indeed,while there isanexactmathematicalsolution toNewton’stheoryfortwoorbitingbodies,thereisnoknowngeneralsolutionforany situation more complicated than this. Not even three bodies. ApplyingNewton’stheorytosystemscomprisinglargecollectionsofgravitatingobjectsisverydifficultandusuallyrequirestheuseofpowerfulcomputerstounderstandwhat is happening. The only exception is when the system involves somesimplifyingsymmetry,suchasasphere,orhascomponentsthataredistributeduniformlythroughspace.

Newton’sgravity is hard enough to apply in realistic situations, butEinstein’stheory is an absolute nightmare. For one thing, instead of Newton’s oneequation,Einsteinhasnolessthanten,whichmustallbesolvedsimultaneously.And each separate equation is muchmore complicated than Newton’s simpleinverse-squarelaw.BecauseoftheequivalencebetweenmassandenergygivenbyE=mc2,allformsofenergygravitate.Thegravitationalfieldproducedbyabody is itself a form of energy, and it also therefore gravitates. This kind ofchicken-and-egg problem is called ‘non-linearity’ by physicists, and it oftenleads to unmanageablemathematical complexitywhen it comes to solving theequations.Thisisthecaseforgeneralrelativity.ExactmathematicalsolutionsofEinstein’sequationsareveryfewandfarbetween.Evenwithspecialsymmetrythetheoryposesgrandchallengesformathematiciansandcomputersalike.

Einsteinknew thathis equationswerehard to solve, and thathewouldnotbeable to make much progress unless he assumed the Universe had somesimplifyingsymmetryoruniformity.In1915relativelylittlewasknownforsureabout the way in which the contents of the Universe were distributed. Manyastronomers felt that theMilkyWaywasan ‘IslandUniverse’;othersbelievedthat it was just one of many such objects scattered more or less uniformlythroughout space. The latter possibility appealedmost to Einstein. TheMilkyWay is an ugly slab of gas, dust, and stars that would be very difficult todescribeproperlyifitwerethewholeUniverse.Thesecondoptionwasbetterinthatitallowedarough-and-readydescriptioninwhichtheMilkyWayandothergalaxies were the fine details in a largely smooth distribution of material.Einstein also had philosophical reasons for preferring large-scale smoothness,stemmingfromanideacalledMach’sprinciple.If theUniversewerethesameeverywherehecouldsethiscosmologicaltheoryonasolidfootingbyallowingthedistributionofmattertodefineaspecialreferenceframethatwouldhelphimdealwiththeeffectsofgravity.

So,withpreciouslittleobservationalevidencetogoon,Einsteindecidedthathewould simplify theUniverse he described bymaking it homogeneous (i.e. thesameineveryplace);atleastonscalesmuchlargerthantheobservedlumpybits(i.e.thegalaxies).HealsoassumedtheUniversetobeisotropic(i.e.lookingthesame in every direction). These twin assumptions together form theCosmologicalPrinciple.

TheCosmologicalPrinciple

The twin assumptions of homogeneity and isotropy are related but notequivalent. Isotropy does not necessarily imply homogeneity without theadditional assumption that the observer is not in a special place. One wouldobserveisotropyinanysphericallysymmetricdistributionofmatter,butonlyifonewereinthemiddle.Acircularcarpetwithapatternconsistingofaseriesofconcentricringswouldlookisotropiconlytoanobserverstandinginthecentreofthepattern.TheprinciplethatwedonotliveinaspecialplaceintheUniverseis called the Copernican Principle, an indication of the debt that moderncosmology owes to history. Observed isotropy, together with the CopernicanPrinciple implies the Cosmological Principle. The Milky Way is clearly notisotropic, as anyonewill knowwhohas looked at the night sky. It occupies adistinctbandacrosstheheavens.AUniverseconsistingonlyoftheMilkyWaycouldthereforenotbeconsistentwiththeCosmologicalPrinciple.

Althoughthename‘CosmologicalPrinciple’soundsgrand,oneshouldhavenoillusionsaboutitsorigin.Moreoftenthannot,Principlesareintroducedinordertoallowsomeprogresstobemadewhenonehasnodatatogoon.Cosmologywas no exception to this rule. It is now known that this guess was basicallycorrect.Inthe1920sitwasestablishedthatthenebulaeweredefinitelyoutsidethe Milky Way, and more recent observational studies of the large-scaledistribution of galaxies and the cosmic microwave background (discussed inChapter7)seemtoindicatetheUniverseissmoothonlargescalesasrequiredbythis idea. It is only more recently that astrophysicists have come up with areasonably convincing argument as to why the Universe has this specialsymmetry.Themysteriousoriginoflarge-scalesmoothnesshasbeencalledthehorizon problem and it is one of the issues addressed by the idea of cosmicinflationdiscussedinChapter8.

Einstein’sbiggestblunder

Armed with the Cosmological Principle, Einstein was able to construct self-consistentmathematicalmodelsof theUniverse. Immediately,however,heraninto a problem. It was an unavoidable consequence of his theory that, in anysolution of his equations in which the Cosmological Principle applies, space-timemustbedynamic.Thismeantthatitwasimpossibleforhimtoconstructamodelofacosmosthatisstaticandunchangingwithtime.HistheoryrequiredtheUniversetobeeitherexpandingorcontracting,althoughitdidn’tsaywhichof these two possibilities would be the case. Einstein didn’t have a greatknowledgeofastronomy,buthehadaskedexpertsaboutthemotionsofdistantstars.Perhapsbecauseheasked thewrongquestion,hegot theanswer thatonaverage the starswereneither approachingnor receding from theSun.This isactually true inside our galaxy, but we now know it is not the case for othergalaxies.

EinsteinwassoconvincedthattheUniverseshouldbestaticthathewentbacktohisoriginalequations.He realized thathecould retain theiressentialcharacterbut introduce a slightmodification thatwould counteract the tendency for hiscosmological models to expand or contract with time. The modification heintroducedwascalledthe‘cosmologicalconstant’.Thisnewterminthetheoryrepresents an alteration of the behaviour of gravity on the very largest scales.Thecosmologicalconstantallowsspaceitselftopossessatendencytoexpandorcontract, and it can be adjusted in the theory so that it exactly balances theexpansionorcontractiontheUniversewouldotherwisebeforcedtopossess.

Satisfiedwith thisfixfor the timebeing,Einsteinwentontoconstructastaticcosmological model, which he published in 1917. Some years later, in 1929,Hubble published the results that led to the acceptance of the idea that theUniversewasnotstaticafterall,butexpanding.Einstein’soriginalmodelisnowonlyofhistorical interest.Without theneed topreventglobal expansion, therewasnoneedforhimtohave introducedthecosmologicalconstant. Inhis lateryears,Einstein referred to this episode as the greatest blunder hehadmade inscience. This comment is usually taken to refer to the cosmological constantitself, but the true blunder was to have failed to predict the expansion of theUniverse.

Althoughuntilrecentlymostcosmologistswerehappynottoincludeitintheir

models, the cosmological constant never really went away. It lurked in thebackgroundlikeamadrelativelivingintheattic.Now,asweshallseeinlaterchapters,ithasbrokenfreefromobscurityandagainplaysaleadingrole.Fortheremainderofthischapter,however,Ishallputittooneside.

TheFriedmannmodels

Einsteinwasnottheonlyscientisttoturntocosmologyintheyearsimmediatelyfollowingthepublicationofthegeneraltheoryofrelativityin1915.OneoftheotherswasanobscureRussianphysicistbythenameofAlexanderFriedmann.ItwasnotEinsteinbutFriedmannwhodevelopedthemathematicalmodelsofanexpandingUniverse,whichformthebasisofthemodernBigBangcosmology.His achievements in this respect are all the more remarkable because heperformedhiscalculationsinconditionsofextremehardshipduringthesiegeofPetrograd. Friedmann died in 1925, before his work (published in 1922) hadachievedanyinternationalrecognition.Stalinlaterliquidatedtheinstitutehehadworked in. Somewhat later a Belgian priest, Georges Lemaître, independentlyobtained the same results, and it is through Lemaître that these ideas wereexploredandamplifiedinWesternEurope.

ThesimplestFriedmannmodelsarethespecialfamilyofsolutionstoEinstein’sequations obtained by requiring that the Cosmological Principle holds, andassuming that there is no cosmological constant. The Cosmological Principleplays a big part in these models. In relativity theory, time and space are notabsolutes. The mathematical description of these two aspects of events (the‘when’andthe‘where’) involvesacomplicatedfour-dimensional‘space-time’,which is hard to conceptualize. In general, Einstein’s theory does not give anunambiguouswayofseparatingspaceandtime.Differentobserverscandisagreeabout the time elapsed between events, depending on theirmotion and on thegravitationalfieldstheyhaveexperienced.IftheCosmologicalPrincipleappliesthenthereisaspecialwaytothinkabouttimethatmakesallthismuchsimpler.If the Universe has the same density everywhere (which it must if it ishomogeneous) then the density ofmatter itself defines a kind of clock. If theUniverseexpands,thenthespacebetweenparticlesincreasesandthedensityofmatter consequently goes down. The later the time, the lower the density ofmatter.Likewise,ahigherdensity impliesanearlier time.Observersanywherein theUniversecanset theirclocksaccording to the localdensityofmatter so

that all these clocks will be perfectly synchronized. and a perfectsynchronization can thereforebe achieved.Themeasureof time that results isusuallycalled‘cosmologicalpropertime’.

Because thedensity is the same in everyplace, and it is thedensityofmatterand/or energy that determines the curvature of space through the Einsteinequations,theCosmologicalPrinciplealsosimplifiesthewayspacecancurveinresponsetogravity.Spacecanbewarped,butitmustbewarpedinthesamewayateverypoint.Thereareinfactonlythreewaysinwhichthiscanhappen.

The obvious way of having the same curvature at every point is to have nocurvature at every point. This is usually called the flat universe. In a flatuniverse, light travels in straight lines and all the laws ofEuclidean geometryapplyjustastheydidinthe‘normal’world.Butifspaceisn’tcurved,whathashappenedtogravity?Thereismatterinaflatuniversesowhydoesitnotwarpspace?Theansweristhatthemassoftheuniversedoeswarpspace,butthisisexactlycounterbalancedbyenergycontained in theexpansionof theUniverse;matterandenergyconspire tonegateeachother’sgravitationaleffects.And inanycase,eventhoughspacemaybeflat,space–timeisstillcurved.

Theflatuniverseisclearlyspecialbecauseitrequiresanexactbalancebetweenthe expansion and the gravitational pull of thematter.When these are not inbalance,therearetwootheralternatives.Iftheuniversehasahighmatterdensitythenthegravitationaleffectofthemasswithinitwins,anditpullsspaceinonitselflikeathree-dimensionalversionofthesurfaceofasphere.Mathematically,the curvature of space is positive in such a situation. In this case, the closeduniverse, light rays actually convergeoneachother.While a flatuniverse canextendindefinitely inalldirections, thecloseduniverse isfinite.Gooff inonedirection and you will come back to where you started from. The otheralternative is theopen universe. This too is infinite, but is harder to visualizethan the closed version because the space curvature is negative. Light raysdivergeinthisexample,asillustratedinthetwo-dimensionalexampleshownintheFigure5.

Thebehaviourofspaceinthesemodelsmirrorsthewaytheyevolveintime.Acloseduniverseisafinitespace,butitalsohasafiniteduration.Iftheuniverseisexpandingatanytimeandisclosed,theexpansionwillslowdowninthefuture.Eventually the universewill stop expanding and recollapse.Theopen and flatmodelswillexpandforever.Gravityalwaysfightstheexpansionoftheuniverse

intheFriedmannmodels,butonlyintheclosedmodeldoesitactuallywin.

TheFriedmannmodelsunderpinmuchofthemodernBigBangtheory,buttheyalso contain the key to its greatest weakness. If we use these calculations toreverse the expansion of theUniverse and turn the clock back on the currentstateofthecosmos,wefindtheuniversegetseverdensertheearlierwego.Ifwetrytogobacktoofar,themathematicsfallapartatasingularity.

Thesingularnatureofgravity

Inmathematics, a singularity is a pathological propertywherein the numericalvalueofaparticularquantitybecomesinfiniteduringthecourseofacalculation.To give a very simplified example, consider the calculation of theNewtonianforceduetogravityexertedbyamassivebodyonanotherparticle.Thisforceisinverselyproportional to thesquareof thedistancebetweenthe twobodies,sothat if one tried to calculate the force for objects at zero separation, the resultwould be infinite. Singularities are not always signs of serious mathematicalproblems. Sometimes they are simply caused by an inappropriate choice ofcoordinates.Forexample,somethingstrangeandakintoasingularityhappensinthestandardmapstobefoundinanatlas.Thesemapslookquitesensibleuntilyoulookverynearthepoles.Ina

5.Open, flat, and closed spaces in two dimensions. In a flat two-dimensionalspace(middle)thelawsofEuclideangeometryholdtrue.Inthiscasethesumofthe angles of a triangle is 180 degrees. In a closed space such as a sphere(bottom), the angles of a triangle come to somewhat more than 180 degrees,whereasforanopenspace(suchasthesaddleshapeshown)it islessthan180degrees.

standard equatorial projection, theNorthPole does not appear as a point as itshould,butisspreadoutfromapointtoastraightlinealongthetopofthemap.But if you were to travel to the North Pole you would not see anythingcatastrophicthere.Thesingularitythatcausesthispointtoappearisanexampleofacoordinatesingularity,anditcanbetransformedawaybyusingadifferent

kindofprojection.Nothingparticularlyoddwillhappentoyouifyouattempttocrossthiskindofsingularity.

Singularities occurwith depressing frequency in solutions of the equations ofgeneral relativity.Someof thesearecoordinatesingularities like theone I justdiscussed. These are not particularly serious. However, Einstein’s theory isspecial in that itpredicts theexistenceof real singularitieswhere realphysicalquantities that should know better, such as the density of matter or thetemperature, become infinite. The curvature of space-time can also becomeinfinite in certain situations. The existence of these singularities suggests tomanythatsomefundamentalphysicsdescribingthegravitationaleffectofmatteratextremedensityisabsentfromourunderstanding.Itispossiblethatatheoryof quantum gravity might enable physicists to calculate what happens deepinsideablackholewithouthavingallmathematicalquantitiesbecominginfinite.Indeed,Einsteinhimselfwrotein1950:

Thetheoryisbasedonaseparationoftheconceptsofthegravitationalfieldandmatter.Whilethismaybeavalidapproximationforweakfields,itmaypresumablybequiteinadequateforveryhighdensitiesofmatter.Onemaynot therefore assume the validity of the equations for very high densitiesand it is just possible that in a unified theory there would be no suchsingularity.

Probablythemostfamousexampleofasingularityliesatthecentreofablackhole.ThisappearsintheoriginalSchwarzschildsolutioncorrespondingtoaholewith perfect spherical symmetry. For many years, physicists thought that theexistence of a singularity of this kind was merely due to the rather artificialspecial nature of this spherical solution.However, in a series ofmathematicalinvestigations,RogerPenroseandothershaveshownthatnospecialsymmetryisrequired and that singularities arisewhenever any objects collapse under theirowngravity.

As if to apologize for predicting these singularities in the first place, generalrelativity does its best to hide them from us. A Schwarzschild black hole issurroundedbyaneventhorizonthateffectivelyprotectsoutsideobserversfromthesingularityitself.Itseemslikelythatallsingularitiesingeneralrelativityareprotected in this way, and so-called naked singularities are not thought to bephysicallyrealistic.

Inthe1960s,however,RogerPenrose’sworkonmathematicalpropertiesoftheblackhole singularitycame to theattentionofStephenHawking,whohad theidea of trying to apply them elsewhere. Penrose had considered what wouldhappen in the futurewhenanobjectcollapsesunder itsowngravity.Hawkingwas interested to know whether these ideas could be applied instead to theproblemofunderstandingwhathadhappenedinthepasttoasystemnowknowntobeexpanding,i.e.theUniverse!HawkingcontactedRogerPenroseaboutthis,andtheyworkedtogetherontheproblemofthecosmologicalsingularity,asitisnowknown.Together theyshowed thatexpanding-universemodelspredict theexistence of a singularity at the very beginning, where the temperature anddensitybecomeinfinite.Nomatterwhethertheuniverseisopen,closed,orflat,thereisafundamentalbarriertoourunderstanding.Inthebeginning,therewasinfinity.

MostcosmologistsinterprettheBigBangsingularityinmuchthesamewayasthe black hole singularity discussed above, i.e. as meaning that Einstein’sequations break down at some point in the earlyUniverse due to the extremephysical conditions present there. If this is the case, then the only hope forunderstanding the early stages of the expansion of the Universe is through abettertheory.Sincewedon’thavesuchatheory,theBigBangisincomplete.Inparticular, since we need to know the total energy budget of the Universe toknowwhetheritisopenorclosed,wecannotdeterminebytheoryalonewhichofthesealternativesis the‘correct’description.Thisshortcomingis thereasonwhy theword ‘model’ is probablymore appropriate than ‘theory’ for theBigBang.TheproblemofnotknowingabouttheinitialconditionsoftheUniverseisthe reasonwhycosmologistsstillcannotanswersomebasicquestions, suchaswhethertheUniversewillexpandforever.

Chapter4TheexpandingUniverse

So far I have concentrated on the way in which developments in theoreticalphysics,particularlythegeneraltheoryofrelativity, ledtomajordevelopmentsincosmologicaltheoryinthe1920s.Butthesenewideasonlygainedacceptancewhen improved observational facilities allowed astronomers to begin makingreliableestimatesof thedistances toandmotionsofgalaxies. In thischapter Iwilldiscusstheseobservations,andhowtheyfitintothetheoreticalframework.

Hubble’sLaw

The nature of the expansion of the Universe is encapsulated in one simpleequation,nowknownastheHubbleLaw.Thisstatesthattheapparentvelocityvofagalaxyawayfromtheobserverisproportionaltoitsdistanced.NowadaystheconstantofproportionalityisknownastheHubbleconstantandisgiventhesymbolH orHo. TheHubbleLaw is thuswritten ‘v =Hod’. The relationshipbetweenvanddiscalledalinearrelationshipbecauseifyouplotagraph(likeHubble did) of themeasured velocities and distances of a sample of galaxies,youfindtheylieonastraightline.TheslopeofthislineisHo.TheHubbleLawbasicallymeans that galaxies twice as far away from the observer aremovingawaytwiceasquickly.Thosethreetimesawaymovethreetimesasfast,andsoon.

6.Hubble’sLaw.Asobservedfromthecentralpoint,Hubble’sLawstatesthatthe apparent recession velocity of distant galaxies is proportional to theirdistance, so the further away they are the quicker they recede. The expansiondoesnothaveacentre:anypointcanbetreatedastheorigin.

Hubblepublishedthediscoveryofhisfamouslawin1929,whichresultedfromastudyofthespectraofasampleofgalaxies.TheAmericanastronomerVestoSlipheralsodeservesalargepartofthecreditforthediscovery.Asearlyas1914Slipherhadobtainedspectraofagroupofnebulae(asgalaxieswerethencalled)that also displayed this relationship, althoughhis distance estimateswere veryrough.Unfortunately, Slipher’s early results, presented at the 17thMeeting oftheAmericanAstronomicalAssociationin1914,wereneverpublished;historyhasneveradequatelyacknowledgedthecontributionSliphermade.

So how did Hubble obtain his law? The technique he used is calledspectroscopy.Lightfromagalaxycontainsamixtureofcolours,producedbyallthestarswithinit.Aspectroscopesplitslightupintoitscomponenthuessothatits precisemixture of colours can be analysed separately.Aprism is a simplewayofachieving thesameend.Withaprismordinarywhite lightcanbesplitinto a spectrum that resembles a rainbow. But as well as having differentcolours, astronomical spectra also contain sharp features called emission lines.Theselinesareproducedinthegascontainedinanobjectbyelectronsshiftingbetweendifferentenergylevels.Thesetransitionsoccuratdefinitewavelengthsdependingon thechemistryof the source; thesewavelengthscanbemeasuredaccuratelyinlaboratoryexperiments.Hubblewasabletoidentifyemissionlines

inmanyofhisgalaxies.Butcomparingtheirpositioninthemeasuredspectrumtowherethelinesshouldbe,hefoundtheywereusuallyinthewrongplace.Infact,thelineswerealmostalwaysshiftedtotheredendofthespectrum,towardslongerwavelengths.HubbleinterpretedthisasaDopplershift.

7. The Hubble diagram. Hubble’s original velocity-distance plot published in1929.Noticethatsomenearbygalaxiesareactuallyapproachingthegalaxy,andthereisconsiderablescatterinhisplot.

Dopplershift

TheDoppler effect was originally introduced to physicswith a fanfare in the1840s.Infactthisisliterallytrue,becausethefirstexperimentaldemonstrationof this effect involved several trumpeters moving on a steam train. Theapplicationinthat instancewastothepropertiesofsoundwaveswhenthereisrelativemotion between the source of the sound and the receiver.We are allfamiliarwith theeffect fromeverydayexperience:anapproachingpolice sirenhasahigherpitchthanarecedingone.Theeasiestwaytounderstandtheeffectistorememberthatthepitchofsounddependsonthewavelengthofthewavesfrom which it is made. High pitch means short wavelength. If a source istravellingnearthespeedofsound,ittendstocatchupthewavesitemitsinfront,thusreducingtheirapparentwavelength.Likewise,ittendstorushaheadofthewavesitemitsbehind,increasingthegapbetweenthewavesandthuslowering

theirapparentpitch.

Intheastronomicalsetting,theDopplereffectappliestolight.Usuallytheeffectis very small, but it becomes appreciable if the velocity of a source is asignificant fraction of the velocity of light. (The Doppler effect for sound issmallunlessthespeedofthecarisreasonablylarge,therelevantscalebeingsetbythespeedofsound.)Amovingsourceofemissiontendstoproducelightofshorterwavelengthifitisapproachingtheobserverandlongerwavelengthifitisreceding.Inthesecasesthelight isshiftedtowardstheblueandredpartsofthe spectrum, respectively. In other words, there is a blueshift (approachingsource)oraredshift(recedingsource).

Ifthesourceisemittingwhitelight,however,onewouldnotbeabletoseeanykindofshift.Supposeeachlinewereredshiftedbyanamountxinwavelength.Thenlightemittedatawavelengthywouldbeobservedatwavelengthy+x.Butthesameamountof lightwouldstillbeobservedat theoriginalwavelengthy,becauselightoriginallyemittedatwavelengthy–xwouldbeshiftedtheretofillthegap.White light thereforestill lookswhite, regardlessof theDopplershift.To see an effect, one has to look at emission lines, which occur at discretefrequenciessothatnosuchcompensationcanoccur.Awholesetoflineswillbeshiftedonewayortheotherinthespectrum,butthelineswillkeeptheirrelativespacing and it is therefore quite easy to identify how far they have shiftedrelativetoasourcewhichisatrestinalaboratory.

Hubblemeasured a larger redshift for themore distant galaxies in his samplethan for thenearbyones.He assumed thatwhat hewas seeingwas aDopplershift,soheconvertedtheshiftingofthespectrallinesintoameasureofvelocity.Whenheplotted this ‘apparent recessionvelocity’ against thedistance, hegothisfamouslinearrelationship.AlthoughHubble’sLawisnowtakentorepresenttheexpansionoftheUniverse,Hubblehimselfnevermadethisinterpretationofhisresults.LemaîtrewasprobablythefirsttheoristtoexplainHubble’sLawinterms of the expansion of the entire Universe. Lemaître’s paper, published in1927,prefiguringHubble’sclassicpaperof1929,hadmadelittleimpressionatthe timebecause itwaswritten inFrenchandpublished inanobscureBelgianjournal. It was not until 1931 that the British astronomer Arthur StanleyEddington hadLemaître’s paper published (inEnglish) in themore influentialMonthly Notices of the Royal Astronomical Society. The identification of theHubbleLawwiththecosmicexpansionisoneofthemainsupportingpillarsofthe Big Bang theory, so Lemaître too deserves great credit for making this

importantstep.

InterpretingtheHubbleLaw

Thefactthatgalaxiesareobservedtobemovingawayfromussuggeststhatwemust be at the centre of the expansion. Doesn’t this violate the CopernicanPrincipleandputusinaspecialplace?Theansweris‘no’.Anyotherobserverwouldalsoseeeverythingmovingaway.Infact,everypointintheUniverseisequivalent as far as the expansion is concerned. Moreover it can be provedmathematically thatHubble’sLawmust apply inahomogeneousand isotropicexpandinguniverse,i.e.oneinwhichtheCosmologicalPrincipleholds.Itistheonlywaysuchauniversecanexpand.

Itmayhelptovisualizethesituationbyreducingthethreedimensionsofspacetothetwo-dimensionalsurfaceofaballoon(thiswouldbeacloseduniverse,butthegeometrydoesnotparticularlymatterforthisillustration).Ifonepaintsdotsontothesurfaceoftheballoonandthenblowsitup,eachdotseesalltheotherdots moving away as if it were the centre of expansion. This analogy has aproblem, however, in that one tends to be aware that the two-dimensionalsurface is embedded in the three dimensions of our ordinary space. Onetherefore sees the centre of the space inside the balloon as the real centre ofexpansion.Thisisinaccurate.OnemustthinkoftheballoonasbeingtheentireUniverse.Itisnotembeddedinanotherspaceandthereisnosuchglobalcentre.Everypointintheballoonisthecentre.Thisdifficultyisoftenalsoconfusedinone’smindwiththequestionofwheretheBigBangactuallyhappened:arewenot moving away from the site of the original explosion? Where was thisexplosion situated? The answer to this is the explosion happened everywhereandeverything ismovingaway from it.But in thebeginning,at theBigBangsingularity,everywhereandeverythingwasinthesameplace.

More than seventy years after Lemaître, the Hubble Law still poses somedifficulties of interpretation.Hubble had notmeasured velocities but redshifts.Theredshift,usuallygiventhesymbolz incosmology,measures thefractionalchange in wavelength of an observed line relative to its expected position.Hubble’sLawissometimesstatedasalinearrelationshipbetweenredshiftzanddistance d, rather than between recession velocity v and d. If the velocitiesconcernedaremuchsmaller than thespeedof lightc then there isnoproblem

becauseinthiscasetheredshiftisroughlythevelocityofthesourcesexpressedasafractionofthespeedoflight.Soifzanddareproportionalandsoarezandv,thenvanddarealso.Butwhentheredshiftsarelargethisrelationshipbreaksdown. What, then, is the correct form to use? In the Friedmann models, theinterpretation of Hubble’s Law is amazingly simple. The linear relationshipbetweenrecessionvelocityvanddistanced, isexactevenwhenthevelocityisarbitrarilylarge.Thismayworrysomeofyou,becauseyouwillhaveheardthatit isnotpossibleforobjectstomovefasterthanlight.InaFriedmannuniversethemoredistant is theobject, thegreater its velocity away from theobserver.The velocity of the object can exceed the speed of light by any amount youplease. It does not violate any principle of relativity, however, because theobservercannotseeit;itisinfinitelyredshifted.

Thereisalsoapotentialprobleminwhatismeantbydandhowtomeasureit.Astronomers cannot usually measure the distance of an object directly. Theycannotextendarulertoadistantgalaxyandcannotusuallyusetriangulationlikesurveyorsdobecausethedistancesinvolvedaretoolarge.Theyhaveinsteadtomakemeasurementsusinglightemittedbytheobject.Sincelighttravelswithafinitespeedand,asweknowthankstoHubble,theUniverseisexpanding,thingsare not at the same position now as theywerewhen light set out from them.Astronomersarethereforeforcedtouseindirectdistancemeasurements,andtoattempt tocorrect for theexpansionof theUniverse to locatewhere theobjectactuallyis.

Butinfactthetheoryhelpsheretoo.Thinkingaboutvelocitiesanddistancesofsourcesisunnecessarilycomplicated.Whiletheredshiftisusuallythoughtofasa Doppler shift, there is another way of picturing this effect, which is muchsimpler and actually more accurate. In the expanding universe, separationsbetweenanypoints increaseuniformly inalldirections. Imagineanexpandingsheetofgraphpaper.Theregulargridonthepaperatsomeparticulartimewilllooklikeablown-upversionofthewayitlookedatanearliertime.Becausethesymmetry of the situation is preserved, one only needs to know the factor bywhichthegridhasbeenexpandedinordertorecoverthepastgridfromthelaterone. Likewise, since a homogeneous and isotropic universe remains so as itexpands,oneonlyneedstoknowanoverall‘scalefactor’toobtainapictureofthepastphysicalconditions frompresentdata.This factor isusuallygiven thesymbola(t)anditsbehaviourisgovernedbytheFriedmannequationsdiscussedinthepreviouschapter.

Remember that light travels with a finite speed. Light arriving now from adistantsourcemusthavesetoutatsomefinite time in thepast.At the timeofemission the Universe was younger than it is now and, since it has beenexpanding,itwassmallerthentoo.IftheUniversehasexpandedbysomefactorbetween the emission of light and its detection at a telescope, the lightwavesemittedwouldbestretchedby thesamefactoras they travelled throughspace.For example, if the universe expanded by a factor three then the wavelengthwould triple. This is a 200 per cent increase and the source consequently isobservedtohaveredshift2.Iftheexpansionfactorwereonlyby10percent(i.e.afactor1.1)thentheredshiftwouldbe0.1,andsoon.Theredshiftisduetothestretchingofspace-timecausedbycosmicexpansion.

8.Redshift.AslighttravelsfromasourcegalaxytotheobserveritgetsstretchedbytheexpansionoftheUniverse,eventuallyarrivingwithalongerwavelengththanwhenitstarted.

Thisinterpretationissosimplethatiteludedphysicistsformanyyears.In1917,WilhemdeSitterhadpublishedacosmologicalmodel inwhichhe found lightrayswouldberedshifted.Becausehehadusedstrangecoordinates inwhichtoexpress his results, he didn’t realize his model represented an expandingUniverseand insteadhe sought toexplainwhathehad foundas somekindofweirdgravitationaleffect.Therewasconsiderableconfusionaboutthenatureofthe‘deSittereffect’formanyyears,butitisnowknowntobeextremelysimple.

It is important also to stress that not everything takes part in the expansion.Objects that are held together by forces other than gravity do not participate.

This includeselementaryparticles, atoms,molecules, and rocks.These insteadremain at a fixedphysical size as theUniverse swells around them.Likewise,objects in which the force of gravity is dominant also resist the expansion.Planet,stars,andgalaxiesareboundsostronglybygravitationalforcesthattheyare not expanding with the rest of the Universe. On scales even larger thangalaxies,notallobjectsaremovingawayfromeachothereither.Forexample,theAndromeda galaxy (M31) is actually approaching theMilkyWay becausethesetwoobjectsareheldtogetherbytheirmutualgravitationalattraction.Somemassiveclustersofgalaxiesaresimilarlyheldtogetheragainstthecosmicflow.Objects larger than thismaynotnecessarilybebound(like individualgalaxiesare), but their gravity may still be strong enough to cause a distortion ofHubble’sLaw.AlthoughthelinearityoftheHubbleLawisnowwellestablishedouttoquitelargedistances,thereisconsiderable‘scatter’aboutthestraightline.Part of this represents statistical errors and uncertainties in the distancemeasurements,butthisisnotthewholestory.Hubble’sLawisonlyexactlytruefor objects moving in an idealized homogeneous and isotropic Universe. OurUniversemaybe roughly like thison largeenoughscales,but it isnotexactlyhomogeneous. Its clumpiness deflects galaxies from the pure ‘Hubble flow’causingthescatterinHubble’splot.

Butonthelargestscalesofall, therearenoforcesstrongenoughtocounteracttheglobaltendencyoftheUniversetoexpandwithtime.Inabroad-brushsense,therefore, ignoring all these relatively local perturbations, allmatter is rushingapartfromallothermatterwithavelocitydescribedbyHubble’sLaw.

9. TheHubble diagram updated. Amore recent compilation of velocities anddistancesbasedonworkbyAllanSandage.Thedistancerangecoveredismuchgreater than in Hubble’s original diagram. The small black rectangle in thebottomleftofthediagramwouldentirelycoverHubble’s1929data.

ThequestforHo

So far I have concentrated on the form of the Hubble Law, and how it isinterpretedtheoretically.ThereisoneotherimportantaspectofHubble’sLawtodiscuss,andthatisthevalueoftheconstantHo.TheHubbleconstantHoisoneofthemostimportantnumbersincosmology,butitisalsoanexampleofoneofthe failingsof theBigBangmodel.The theory cannotpredictwhatvalue thisimportant number should take; it is part of the information imprinted at thebeginningoftheUniversewhereourtheorybreaksdown.ObtainingatruevalueforHo using observations is a very complicated task. Astronomers need twomeasurements. First, spectroscopic observations reveal the galaxy’s redshift,indicating its velocity. This part is relatively straightforward. The secondmeasurement,thatofthedistance,isbyfarthemoredifficulttoperform.

Supposeyouwereinalargedarkroominwhichthereisalightbulbplacedatanunknowndistance fromyou.Howcould youdetermine its distance?Onewaywould be to attempt to use some kind of triangulation. You could use asurveying device such as a theodolite,moving around in the room,measuringanglestothebulbfromdifferentpositions,andusingtrigonometrytoworkoutthedistance.Analternativeapproachistomeasuredistancesusingthepropertiesofthelightemittedbythebulb.Supposeyouknewthatthebulbwas,say,a100-watt bulb. Suppose also that you were equipped with a light meter. Bymeasuring the amount of light you receive using the light meter, andrememberingthattheintensityoflightfallsoffasthesquareofthedistance,youcouldinferthedistancetothebulb.Ifyoudidn’tknowinadvancethepowerofthebulb,however,thismethodwouldnotwork.Ontheotherhand,ifthereweretwo identical bulbs in the roomwith unknown but identicalwattage then youcould tell therelativedistancesbetweenthemquiteeasily.Forexample, ifone

bulbproducedareadingonyourlightmeterthatwasfourtimessmallerthanthereadingproducedbytheotherbulbthenthefirstbulbmustbetwiceasfarawayasthesecond.Butyoustilldon’tknowinabsolutetermshowfaritistoeitherofthebulbs.

Putting these ideas into an astronomical setting highlights the problems ofdeterminingthedistancescaleoftheUniverse.Triangulationisdifficultbecauseitisnotfeasibletomoveverymuchrelativetothedistancesconcerned,exceptin special situations (see below). Measuring absolute distances using stars orother sources is also difficult unless we can find someway of knowing theirintrinsicluminosity(orpoweroutput).Afeeblestarnearbylooksthesameasaverybrightstarfaraway,sincestars,ingeneral,cannotberesolvedevenbythemost powerful telescopes. If we know that two stars (or other sources) areidentical,however,thenmeasuringrelativedistancesisnotsodifficult.Itisthecalibrationoftheserelativedistancemeasuresthatformsthecentraltaskofworkontheextragalacticdistancescale.

Toput thesedifficulties intoperspective,oneshould remember that itwasnotuntil the 1920s that therewas even a rough understanding of the scale of theUniverse.PriortoHubble’sdiscoverythatthespiralnebulae(astheywerethencalled)wereoutside theMilkyWay, the consensuswas that theUniversewasactuallyverysmallindeed.Thesenebulae,nowknowntobespiralgalaxiesliketheMilkyWay,wereusuallythoughttorepresenttheearlystagesofformationof structures likeourSolarSystem.WhenHubble announced thediscoveryofhiseponymous law, thevalueofHoheobtainedwasabout500kilometrespersecond per Megaparsec (the usual units in which the Hubble constant ismeasured).This is about eight times larger thancurrent estimates.Hubblehadmadeamistake in identifyingakindofstar touseasadistance indicator (seebelow) and, when his error was corrected in the 1950s by Baade, the valuedroppedtoabout250inthesameunits.Sandage,in1958,revisedthevaluestillfurthertobetween50and100andpresentobservationalestimatesstilllieinthisrange.

ModernmeasurementsofHouseabatteryofdistanceindicators,eachonetakingone step upwards in scale, starting with local estimates of distances to starswithin theMilkyWay, and ending at themostdistant galaxies and clustersofgalaxies.Thebasicidea,however,isstillthesameasthatpioneeredbyHubbleandSandage.

First,oneexploitslocalkinematicdistancemeasurestoestablishthescaleoftheMilkyWay. Kinematic methods do not rely upon knowledge of the absoluteluminosity of a source, and they are analogous to the idea of triangulationmentioned above. To start with, distances to relatively nearby stars can begaugedusing the trigonometric parallax of a star, i.e. the change in the star’spositionon thesky in thecourseofayeardue to theEarth’smotion inspace.The usual astronomers’ unit of distance – the parsec (pc) – stems from thismethod:astaroneparsecawayproducesaparallaxofonesecondofarcwhentheEarthmovesfromonesideoftheSuntotheother.Forreference,oneparsecis around three lightyears.The important astrometric satelliteHipparchoswasabletoobtainparallaxmeasurementsforthousandsofstarsinourgalaxy.

Another important classofdistance indicators containsvariable starsofwhichthemost important are the Cepheid variables. The variability of these objectsgives clues about their intrinsic luminosity. The classical Cepheids are brightvariable starsknown todisplayavery tight relationshipbetween theperiodofvariationPandtheirabsoluteluminosityL.ThemeasurementofPforadistantCepheidthusallowsonetoestimateitsL,andhenceitsdistance.Thesestarsaresobrightthattheycanbeseeningalaxiesoutsideourownandtheyextendthedistance scale toaround4Mpc (4,000,000pc).Errors in theCepheiddistancescale,duetointerstellarabsorption,galacticrotation,and,aboveall,aconfusionbetween Cepheids and another type of variable star, called the W Virginisvariables,wereresponsibleforHubble’slargeoriginalvalueforHo.Otherstellardistance indicators allow the ladder tobeextended slightly toaround10Mpc.Collectively,thesemethodsaregiventhenameprimarydistanceindicators.

Thesecondarydistance indicators includeHIIregions(largecloudsof ionizedhydrogen surrounding very hot stars) and globular clusters (clusters of aroundonehundredthousandtotenmillionstars).Theformerofthesehasadiameter,andthelatteranabsoluteluminosity,whichhasasmallscatteraroundthemeanfor these objects. With such relative indicators, calibrated using the primarymethods,onecanextendthedistanceladderouttoabout100Mpc.Thetertiarydistanceindicatorsincludebrightestclustergalaxiesandsupernovae.Clustersofgalaxiescancontainuptoaboutathousandgalaxies.Onefindsthatthebrightestellipticalgalaxyinarichclusterhasaverystandardtotal luminosity,probablybecausetheseobjectsareknowntobeformedinaspecialwaybycannibalizingother galaxies.With the brightest galaxies one can reach distances of severalhundredMpc.Supernovaearestarsthatexplode,producingaluminosityroughlyequaltothatofanentiregalaxy.Thesestarsarethereforeeasilyseenindistant

galaxies.Manyother indirectdistanceestimateshavealsobeenexplored, suchascorrelationsbetweenvariousintrinsicpropertiesofgalaxies.

10.TheHubbleSpaceTelescope.ThisphotographwastakenastheshuttlewasdeployedfromtheSpaceShuttlein1990.OneofthemostimportantprojectstheHubble Telescope has undertaken has been to measure distances to stars indistantgalaxiesinordertomeasureHubble’sconstant.

SothereseemstobenoshortageoftechniquesformeasuringHo.WhyisitthenthatthevalueofHoisstillknownsopoorly?Oneproblemisthatasmallerrorinone rung of the distance ladder also affects higher levels of the ladder in acumulativeway.Ateach level therearealsomanycorrections tobemade: theeffect of galactic rotation in the Milky Way; telescope aperture variations;absorption and obscuration in the Milky Way; and observational biases ofvariouskinds.Giventhelargenumberofuncertaincorrections,itisperhapsnotsurprising that we are not yet in a position to determine Ho with any greatprecision. Controversy has surrounded the distance scale ever since Hubble’sday.Anend to this controversy seems tobe in sight, however,becauseof thelatest developments in technology. In particular, the Hubble Space Telescope(HST)isabletoimagestars,particularlyCepheidvariables,directlyingalaxieswithintheVirgoclusterofgalaxies,anabilitywhichbypassesthemainsourcesofuncertainty in thecalibrationof traditional steps in thedistance ladder.The

HST key programme on the distance scale is expected to fix the value ofHubble’sconstant toanaccuracyofabout10percent.Thisprogramme isnotyetcomplete,butlatestestimatesaresettlingonavalueofHointherange60to70kilometrespersecondperMegaparsec.

11.Cepheids inM100.These pictureswere takenwith theHubbleTelescope;the three images indicate the presence of a variable star now known to be aCepheid.Hubblehasbeenable tomeasure thedistance to thisgalaxy,directlybypassingtheindirectmethodsinusepriortothelaunchofthistelescope.

TheageoftheUniverse

IftheexpansionoftheUniverseproceededataconstantratethenitwouldbeaverysimplemattertorelatetheHubbleconstanttotheageoftheUniverse.Allthegalaxiesarenowrushingapart,butinthebeginningtheymusthaveallbeeninthesameplace.Allweneedtodoisworkoutwhenthishappened;theageoftheUniverse is then the timeelapsedsince thisevent. It’saneasycalculation,and it tells us that the age of the Universe is just the inverse of the Hubble

constant.ForcurrentestimatesofHo theageoftheUniverseworksoutaround15billionyears.

This calculationwouldonlybe true, however, in a completely emptyuniversethatcontainednomattertocausetheexpansiontoslowdown.IntheFriedmannmodels, the expansion is decelerated by an amount depending on how muchmatter there is in the Universe. We don’t really know exactly how muchdecelerationneeds tobe allowed for, but it’s clear the agewill alwaysbe lessthanthevaluewejustcalculated.Iftheexpansionisslowingdown,itmusthavebeenfasterinthepast,sotheuniversemusthavetakenlesstimetogettowhereitis.Theeffectofdecelerationis,however,notparticularlylarge.Theageofaflatuniverseshouldbeabout10billionyears.

AnindependentmethodforestimatingtheageoftheUniverseistodateobjectswithin it.Obviously, since theBigBang represents the origin of allmatter aswellasofspace-time,thereshouldbenothingintheUniversethatisolderthanthe Universe. Dating astronomical objects is, however, not easy. One canestimate ages of terrestrial rocks using the radioactive decay of long-livedisotopes, such as uranium-235, which have a half-lifemeasured in billions ofyears.Themethod iswell understood and similar to the archaeological use ofradiocarbon dating, with the only difference being the vastly larger timescaleneededforthecosmologicalapplicationrequiringtheuseofelementswithmuchlongerhalf-livesthancarbon-14.Thelimitationofsuchapproaches,however,isthattheycanonlybeusedtodatematerialwithintheSolarSystem.Lunarandmeteoritic rocks are older than terrestrialmaterial, but theymay have formedveryrecentlyindeedduringthehistoryoftheUniversesoarenotuseful inthecosmologicalsetting

12. The age of theUniverse.Whether they are open, flat, or closed the usualFriedmannmodelsarealwaysslowingdown.ThismeansthattheHubbletime,1/Ho,alwaysexceedstheactualtimeelapsedsincetheBigBang(to).

ThemostusefulmethodformeasuringtheageoftheUniverseislessdirect.Thestrongest constraints come from studies of globular star clusters. The stars intheseclustersarethoughttohaveallformedatthesametime,andthefactthatthey generally are stars of very low mass suggests that they are quite old.Becausetheyallformedatthesametime,acollectionofthesestarscanbeusedtocalculatehowtheyhavebeenevolving.ThisputsalowerlimitontheageoftheUniverse,becauseonemustallowsometimesincetheBigBangtoformtheclustersinthefirstplace.Recentstudiessuggestthatsuchsystemsarearound14billionyearsold,thoughthishasbecomecontroversialinrecentyears.Onecansee that this poses immediate problems for the flat universe model. Globularclusterstarsaresimplytoooldtofitintheshortlifetimeofsuchauniverse.Thisargumenthaslentsomesupporttotheargumentthatweinfactliveinanopenuniverse.Morerecently,andmoreradically,theagesofoldstarsalsoseemtofitneatly with other evidence suggesting the Universe might have been beenspeedingupratherthanslowingdown.I’lldiscussthismoreinChapter6.

Chapter5TheBigBang

WhilethebasictheoreticalframeworkoftheFriedmannmodelshasbeenaroundfor many years, the Big Bang has emerged only relatively recently as thelikeliestbroad-brushaccountofhowthecontentsoftheUniversehaveevolvedwith time. For many years, most cosmologists favoured an alternative modelcalled the Steady State model. Indeed, the Big Bang itself had a number ofvariants.Amoreprecisephrasingofthemoderntheoryistocallitthe‘hotBigBang’ to distinguish it from an older rival (now discarded),which had a coldinitialphase.AsIhavementionedalready, it isalsonotentirelycorrect tocallthisa‘theory’.Thedifferencebetweentheoryandmodelissubtle,butausefuldefinitionisthatatheoryisusuallyexpectedtobecompletelyself-contained(itcanhavenoadjustableparameters,andallmathematicalquantitiesaredefinedapriori)whereasamodelisnotcompleteinthesameway.OwingtotheuncertaininitialstagesoftheBigBang,itisdifficulttomakecast-ironpredictionsanditisconsequentlynoteasy to test.Advocatesof theSteadyState theoryhavemadethis criticismonmanyoccasions. Ironically, the term ‘BigBang’was initiallyintended to be derogatory andwas coined in a BBC radio programme by SirFredHoyle,onethemodel’smostprominentdissidents.

SteadyStatetheory

In theSteadyStatecosmologicalmodel,advancedbyGold,Hoyle,Bondi,andNarlikar (amongst others), the universe is expanding but nevertheless has thesamepropertiesatalltimes.TheprinciplebehindthistheoryiscalledthePerfectCosmologicalPrinciple,ageneralizationoftheCosmologicalPrinciplethatsaysthat the Universe is homogeneous and isotropic in space to include also

homogeneitywithrespecttotime.

BecauseallthepropertiesofSteadyStatecosmologyhavetobeconstantintimetheexpansionrateofthismodelisalsoaconstant.Itispossibletofindasolutionof the Einstein equations that corresponds to this. It is called the de Sittersolution.But if theUniverse isexpanding, thedensityofmattermustdecreasewithtime.Ormustit?TheSteadyStatetheorypostulatestheexistenceofafield,calledtheC-field,whichcreatesmatteratasteadyratetocounteractthedilutioncausedbycosmicexpansion.Thisprocess,calledcontinuouscreation,hasneverbeen observed in the laboratory but the rate of creation required is so small(aboutoneatomofhydrogenpercubicmetreintheageoftheUniverse)thatitisdifficulttoruleoutcontinuouscreationasapossiblephysicalprocessbydirectobservation.

TheSteadyStatewasabettertheoryintheeyesofmanytheoristsbecauseitwaseasier to test than its rivals. Inparticular,anyevidenceatall that theUniversewasdifferentinthepasttowhatitislikenowwouldruleoutthemodel.Fromthe late 1940s onward, observers attempted to see if the properties of distantgalaxies (whichone sees as theywere in thepast)weredifferent fromnearbyones. Such observations were difficult and problems of interpretation led toacrimoniousdisputesbetweenadvocatesoftheSteadyStatetheoryanditsrival,exemplifiedbyabitterfeudbetweentheradioastronomerMartinRyleandFredHoyle when the former claimed to have found significant evolution in radiosource properties. It was not until themid-1960s that an accidental discoveryshedindependentandcruciallightontheargument.

Thesmokinggun

Intheearly1960stwophysicists,ArnoPenziasandRobertWilson,wereusingacurious horn-shaped microwave antenna left over from telecommunicationssatellite tests to study the emission produced by the Earth’s atmosphere. Thetelescopehadbeendesignedtostudypossiblesourcesofinterferencethatmightcause problems for planned satellite communication systems. Penzias andWilsonweresurprisedtofindauniformbackgroundofnoise,whichwouldnotgoaway.Eventually,aftermuchcheckingandtheremovalofpigeonsthathadbeennestingintheirtelescope,theyacceptedthatthenoisewasnotgoingtogoaway.Coincidentally, just down the road inPrincetonNew Jersey, a groupof

astrophysicists includingDickeandPeebleshadbeen trying toget together anexperimenttodetectradiationproducedbytheBigBang.Theyrealizedtheyhadbeenbeatentoit.PenziasandWilsonpublishedtheirresultintheAstrophysicalJournal in 1965, alongside a paper from the Dicke group explaining what itmeant.PenziasandWilsonwereawardedtheNobelPrizein1978.

Since its discovery the microwave background has been subject to intensescrutiny, and we now know much more about it than was the case in 1965.PenziasandWilsonhadnoticed that theirnoisedidnotdependon the timeofday,whichonewouldexpectifitwereanatmosphericphenomenon.Indeedthevery high degree of uniformity of themicrowave background radiation showsthatitisnotevenassociatedwithsourceswithinourgalaxy(whichwouldnotbedistributedevenlyonthesky).Itisdefinitelyanextragalacticbackground.Moreimportantly, it is now known that this radiation has a very particular kind ofspectrumcalledablackbody.Black-bodyspectraarisewhenever thesource isbothaperfectabsorberandaperfectemitterofradiation.Theradiationproducedbyablackbodyisoftencalledthermalradiation,becausetheperfectabsorptionandemissionbringsthesourceandtheradiationintothermalequilibrium.

13.Thespectrumof thecosmicmicrowavebackground.Thisgraphshows themeasured intensity of the cosmic microwave background as a function ofwavelength.Boththeoryandmeasurementareplottedhere;theagreementissogood that the two curves lie on top of one another. This perfect black-bodybehaviouristhestrongestevidencethattheUniversebeganwithahotBigBang.

Thecharacteristicblack-bodyspectrumofthisradiationdemonstratesbeyondallreasonabledoubtthatitwasproducedinconditionsofthermalequilibriumintheveryearlystagesof theprimordialfireball.Themicrowavebackgroundisnowverycold:itstemperatureisjustlessthanthreedegreesaboveabsolutezero.Butthis radiation has gradually been cooling as an effect of the expansion of theUniverse,aseachconstituentphotonsuffersaredshift.Turningtheclockbacktoearlier stages of the Universe’s evolution, these photons get hotter and carrymoreenergy.Eventuallyonereachesastagewhere the radiationstarts tohavehadadrasticeffectonmatter.Ordinarygasismadefromatomsthatconsistofelectrons orbiting around nuclei. In an intense radiation field, however, theelectrons are stripped off to form a plasma in which the matter is said to beionized. This would have happened about 300,000 years after the Big Bang,whenthetemperaturewasseveralthousanddegreesandtheUniversewasaboutone thousand times smaller and abillion timesdenser than it is today.At thisperiod the entire Universe was as hot as the surface of the Sun (which,incidentally,alsoproducesradiationofnearblack-bodyform).Underconditionsof complete ionization, matter (especially the free electrons) and radiationundergo rapid collisions that maintain thermal equilibrium. The Universe istherefore opaque to light when it is ionized. As it expands and cools, theelectronsandnucleirecombineintoatoms.Whenthishappens,photonscatteringismuch less efficient. In fact theUniverse becomes virtually transparent afterrecombination,sowhatweseeas themicrowavebackgroundtoday is thecoolrelicradiationthatwaslastscatteredbyelectronsattheepochofrecombination.Whenitwasfinallyreleasedfromscatteringprocesses,thisradiationwouldhavebeenintheopticalorultravioletpartofthespectrum,butsincethattimeithasbeenprogressivelyredshiftedbytheexpansionoftheUniverseandisnowseenatinfraredandmicrowavewavelengths.

Because of its near-perfect isotropy on the sky, the cosmic microwavebackgroundprovidessomeevidenceinfavouroftheCosmologicalPrinciple.Italso provides clues to the origin of galaxies and clusters of galaxies. But itsimportance in the framework of the Big Bang theory far exceeds these. Theexistence of the microwave background allows cosmologists to deduce theconditionspresent in theearly stagesof theBigBangand, inparticular,helpsaccountforthechemistryoftheUniverse.

Nucleosynthesis

ThechemicalcompositionoftheUniverseisbasicallyverysimple.Thebulkofknowncosmicmaterialisintheformofhydrogen,thesimplestofallchemicalmaterials,containinganucleusofasingleproton.Morethan75percentofthematterintheuniverseisinthissimpleform.Asidefromthehydrogen,about25percentofthematerialconstituents(bymass)oftheUniverseisintheformofhelium-4,astableisotopeofheliumwhichhastwoprotonsandtwoneutronsinits nucleus.About onehundred thousand times rarer than this come twomoreexoticelements.Deuterium,orheavyhydrogenasit issometimescalled,hasanucleusconsistingofoneprotonandoneneutron.Thelighterisotopeofhelium,helium-3, is short of oneneutron compared to its heavier version.And finallythere comes lithium-7, produced as a tiny trace elementwith an abundanceofonepartintenbillionoftheabundanceofhydrogen.Howdidthischemicalmixcomeabout?

Ithasbeenknownsincethe1930sthatstarsworkbyburninghydrogenasakindof nuclear fuel. As part of this process, stars synthesize helium and otherelements.ButweknowthatstarsalonecannotberesponsibleforproducingthecocktailoflightelementsIhavejustdescribed.Foronething,stellarprocessesgenerally involveadestructionofdeuteriummorequickly than it isproduced,becausethestrongradiationfieldsinstarsbreakupdeuteriumintoitscomponentprotonsandneutrons.Elementsheavierthanhelium-4aremaderathereasilyinstellar interiors but the percentage of helium-4 observed is too high to beexplainedbytheusualpredictionsofstellarevolution.

It is interesting that the difficulty of explaining the abundance of helium bystellarprocessesalonewas recognizedasearlyas the1940sbyAlpher,Bethe,and Gamow who themselves proposed a model in which nucleosynthesisoccurred in the early stages of cosmological evolution. Difficulties with thismodel, in particular an excessive production of helium, persuadedAlpher andHerman in 1948 to consider the idea that theremight have been a significantradiationbackgroundat theepochofnucleosynthesis.Theyestimated that thisbackgroundshouldhaveapresent temperatureofaround5K,notfarfromthevalue it is nowknown to have, although some fifteen yearswere to intervenebeforethecosmicmicrowavebackgroundradiationwasdiscovered.

Thecalculationoftherelativeamountsoflightnucleiproducedintheprimordial

fireball requires a few assumptions to be made about some properties of theUniverse at the relevant stage of its evolution. In addition to the normalassumptionsgoingintotheFriedmannmodels,itisnecessaryalsotorequirethattheearlyUniversewentthroughastageofthermalequilibriumattemperaturesofmorethanabilliondegrees.IntheBigBangmodelthiswouldhavehappenedveryearlyonindeed,withinafewsecondsofthebeginning.Otherthanthat,thecalculationsarefairlystraightforwardandtheycanbeperformedusingcomputercodesoriginallydevelopedformodellingthermonuclearexplosions.

Before nucleosynthesis begins, protons and neutrons are continuallyinterconvertingbymeansofweaknuclear interactions(thenuclear interactionsaredescribedinmoredetailabitlateron).Therelativenumbersofprotonsandneutronscanbecalculatedaslongastheyareinthermalequilibriumand,whilethe weak interactions are fast enough to maintain equilibrium, the neutron-proton ratio continually adjusts itself to the cooling surroundings. At somecritical point, however, theweak nuclear reactions become inefficient and theratiocannolongeradjust.Whathappensthenisthattheneutron-protonratiois‘frozenout’ataparticularvalue(aboutoneneutronforeverysixprotons).Thisratio is fundamental in determining the eventual abundance of helium-4. Tomake helium by adding protons and neutrons together, we first have tomakedeuterium.But I have alreadymentioned that deuterium is easilydisruptedbyradiation.Ifadeuteriumnucleusgetshitbyaphoton,itfallsapartintoaprotonandneutron.WhentheUniverseisveryhot,anydeuteriumisdestroyedassoonasitismade.

Thisiscalledthedeuteriumbottleneck.Whilethisnucleartrafficjamexists,noheliumcanbemade.Moreover,theneutronswhichfrozeoutbeforethisstarttodecaywithalifetimeofaroundtenminutes.Theresultofthedelayisthereforethatslightlyfewerneutronsareavailableforthesubsequentcookingofhelium.

When the temperature of the radiation bath falls below a billion degrees, theradiationisnotstrongenoughtodissociatedeuteriumanditlingerslongenoughforfurtherreactionstooccur.Twodeuteriumnucleicanweldtogethertomakehelium-3, with the ejection of a neutron. Helium-3 can capture a deuteriumnucleusandmakehelium-4andejectaproton.Thesetworeactionshappenveryquicklywith the result thatvirtuallyallneutronsendup inhelium-4,andonlytracesoftheintermediatedeuteriumandhelium-3areproduced.Theabundanceby mass of helium-4 that comes out naturally is about 25 per cent, just asrequired. Likewise, the amounts of intermediate nuclei are also close to the

observations.Allthisisdoneinthefirstfewminutesoftheprimordialfireball.

This seems like a spectacular success of the theory, which it is indeed. Butagreement between detailed calculations of the nuclear fallout from the BigBangandobservedelementabundancesisonlyreachedforaparticularvalueofone crucial parameter, the baryon-to-photon ratio of the Universe. The wholethingonlyworksifthisnumberisaroundoneintenbillion.Thatisoneprotonorneutronforeverytenbillionphotons.Wecanusetheknowntemperatureofthe microwave background to work out how many photons there are in theUniverse. This can be done very accurately. Since we know the baryon-to-photonratiorequiredtomakenucleosynthesisworkwecanusetheappropriatevalue to calculate the number of baryons. The result is tiny. The amount ofmatterintheformofbaryonscanonlybeafewpercentoftheamountofmassrequiredtoclosetheUniverse.

Turningbacktheclock

Theproductionofthemicrowavebackgroundduringtheepochofrecombinationand the synthesis of the elements during the nuclear fireball are two majorsuccesses of the Big Bang theory. The way observations tally with detailedcalculations provides firm support for the model. Buoyed by these successes,cosmologistshavesincetriedtousetheBigBangtoexploreotherconsequencesofmatter at very high density and temperature. In this activity, theBigBangexploitstheconnectionbetweentheworldoftheverylargeandthatoftheverysmall.

Thefurtherintothepastwetravel,thesmallerandhottertheUniversebecomes.Weare livingnowat anepochabout15billionyearsafter theBigBang.Themicrowavebackgroundwasproducedabout300,000yearsafter theBigBang.The nuclear furnace did its cooking in the first few minutes. Pushing ourunderstandingoftheUniversetoearliertimesrequiresknowledgeofhowmatterbehavesatenergiesabove thoseachieved innuclear reactors.Experiments thatcan probe such phenomenal scales of energy can only be constructed atenormous cost. Particle accelerators such as those at CERN in Geneva canrecreatesomeaspectsoftheprimevalinferno,butourknowledgeofhowmatterbehavesundertheseextremeconditionsisstillfragmentaryanddoesnotextendtomuchearlierperiodsthantheepochofnucleosynthesis.

IntheearlydaysphysicistssawtheBigBangasaplacewheretheycouldapplytheir theories. Now, with theories of particle physics still largely untestedelsewhere, it has become a testing-ground.To see how this has happened,wehavetounderstandthedevelopmentofparticlephysicsoverthelastfortyyears.

14. Looking back in time.Aswe look further out into space,we look furtherbackintime.Relativelynearbyweseegalaxies.Furtherawaywecanseehighlyactive galaxies known as quasars. Beyond that there are the ‘dark ages’: thelook-back time is so great that we are viewing the Universe before galaxiesformed.Eventuallywe look so far that theUniversewas sohot that itwasanopaquefireballmuchlikethecentralpartsofastar.ThefireballradiationcomestousthroughtheexpandingUniverseandarrivesasthemicrowavebackground.Ifwecouldseefurtherthanthis,wewouldseenuclearreactionshappening,astheydo in stars.At earlier times the energiesbecome sohigh thatwehave torelyonguesswork.Finally,wereachtheedgeoftheUniverse…whenquantum

gravitybecomesimportantweknownothing.

Thefourforcesofnature

Armedwiththenewtheoriesofrelativityandquantummechanics,andinmanycases further spurred on by new discoveries made possible by advances inexperimental technology, physicists in this century have sought to expand thescope of science to describe all aspects of the natural world. All phenomenaamenabletothistreatmentcanbeattributabletotheactionsofthefourforcesofnature.These four fundamental interactions are theways inwhich the variouselementary particles fromwhich allmatter ismade interactwith each other. Ihave already discussed two of these, electromagnetism and gravity. The othertwoconcerntheinteractionsbetweentheconstituentsofthenucleiofatoms,theweaknuclearforceandthestrongnuclearforce.Thefourforcesvaryinstrength(gravityistheweakest,andthestrongnuclearforceisthestrongest)andalsointhekindsofelementaryparticlesthattakepartintheinteractionstheycontrol.

Theelectromagnetic forceholdselectrons inorbit aroundatomicnuclei and isthus responsible for holding together all material with whichwe are familiar.However, itwas realized early in the twentieth century that, in order to applyMaxwell’stheoryindetail toatoms,ideasfromquantumphysicsandrelativitywouldhave tobe incorporated. Itwasnotuntil theworkofRichardFeynmanand others, building on the work of Dirac, that a full quantum theory of theelectromagnetic force, calledquantumelectrodynamics,wasdeveloped. In thistheory, usually abbreviated to QED, electromagnetic radiation in the form ofphotons is responsible for carrying the electromagnetic interaction betweenparticlesofdifferentcharges.

Before discussing interactions any further it is worthmentioning some of thepropertiesoftheelementaryparticlesbetweenwhichtheseforcesact.Thebasicpropertiesareparticlescalled fermions.Thesearedistinguished from the forcecarriers,thebosons(suchasthephoton),bytheirspin.Thefermionsaredividedintotwoclasses,theleptonsandthequarks,eachoftheseclassesisdividedintothree generations, and each generation contains two particles. Altogether,therefore,therearesixleptons(arrangedinthreepairs).Oneofeachleptonpair

ischarged(theelectronisanexample),whiletheothercarriesnochargeandiscalled a neutrino.While the electron is stable, the other two charged leptons(calledthemuandthetau)decayveryrapidlyandareconsequentlymuchmoredifficulttodetect.

Thequarksareall chargedand the three familiesof themarealsoarranged inpairs.The first familycontains the ‘up’and the ‘down’; the secondpair is the‘strange’andthe‘charmed’; the thirdcontains the‘bottom’andthe‘top’.Freequarks are not observed, however. They are always confined into compositeparticles called hadrons. These particles include the baryons, which arecombinations of three quarks, the most familiar examples of which are theprotonandtheneutron.Therearemanyotherhadronstates,butmostofthemareveryunstable.Theymightbeproducedinacceleratorexperiments(orintheBigBang) but do not hang around for long before decaying. Using our currentunderstandingitseemsthatwithinonemillionthofasecondofthebeginningoftimequarkshavesufficientenergytotearthemselvesfree.Atearliertimesthanthis,thefamiliarhadronicparticlesdissolveintoa‘soup’ofquarks.

Eachofthefermionsalsohasamirror-imageversioncalleditsantiparticle.Theantiparticle of the electron is the positron; there are also antiquarks andantineutrinos.

The theory ofQED describes interactions between the charged fermions. Thenext force to come under the spotlight was the weak nuclear force, which isresponsiblefor thedecayofcertainradioactivematerials.Theweakinteractioninvolvesallkindsof fermions including theneutrinoswhich,beinguncharged,cannot feel the QED interaction. As in the case of electromagnetism, weakforces between particles aremediated by other particles – not photons, in thiscase,butmassive

15.Buildingblocksofmatter.Thestandardmodelofparticlephysicsconsistsofarelativelysmallnumberofbasicparticles.Therearequarksarrangedinthreegenerations each of which contains two particles; heavy nuclear particles aremadeofsuchquarks.Theleptonsarearrangedinasimilarfashion.Thequarksandthe leptonsarefermions, forcesbetween themaremediatedbybosons(ontheright)calledthephoton,thegluons,andtheweakWandZbosons.

particles called theW and Z bosons. The fact that these particles have mass(unlike thephoton) is the reasonwhy theweaknuclear forcehas sucha shortrangeanditseffectsareconfinedtothetinyscalesofanatomicnucleus.TheWandZparticlesotherwiseplaythesameroleinthiscontextasthephotondoesinQED:they,andthephoton,areexamplesofwhatareknownasgaugebosons.

Thetheoryofthestronginteractionsresponsibleforholdingthequarkstogetherin hadrons is called quantum chromodynamics (or QCD) and it is built uponsimilar lines toQED.InQCD, there isanothersetofgaugebosons tomediatetheforce.Thesearecalledgluons;thereareeightofthem.InadditionQCDhasapropertycalled‘colour’whichplaysasimilarroletothatofelectricchargeinQED.

Thedriveforunification

Is itpossible, takingacue fromMaxwell’s influentialunificationofelectricityandmagnetism in the19thcentury, toputallQED, theweak interactions,andQCDtogetherinasingleoverarchingtheory?

Atheorythatunifiestheelectromagneticforcewiththeweaknuclearforcewasdeveloped around 1970 by Glashow, Salaam, and Weinberg. Called theelectroweak theory, this represents these two distinct forces as being the low-energymanifestationsofasingleforce.Whenparticleshavelowenergy,andaremovingslowly,theydofeelthedifferentnatureoftheweakandelectromagneticforces. Physicists say that at high energies there is a symmetry between theelectromagnetic and weak interactions: electromagnetism and the weak forceappeardifferenttousatlowenergiesbecausethissymmetryisbroken.Imagineapencilstandingonitsend.Whenverticalitlooksthesamefromalldirections.Arandomairmovementorpassinglorrywillcauseittotopple:itcouldfallinanydirectionwithequalprobability.Butwhen it falls, it falls someparticularway picking out some specific direction. In the same way, the differencebetweenelectromagnetismandweaknuclearforcescouldbejusthappenstance,a chance consequence of how the high-energy symmetry was broken in ourworld.

The electroweak and strong interactions coexist in a combined theory of thefundamentalinteractionscalledthestandardmodel.It’sanamazingsuccessthatall the principal particles predicted by the standard model have now beendiscovered, with only one exception. (A special boson, called the Higgs, isrequired to explain themasses in the standardmodel and it has so far defieddetection.) This model, however, does not provide a unification of all threeinteractionsin thesamewaythat theelectroweaktheorydoesfor twoof them.Physicistshopeeventually tounifyall threeof the forcesdiscussedso far inasingletheory,whichwouldbeknownasaGrandUnifiedTheory,orGUT.Therearemany contenders for such a theory, but it is not knownwhich (if any) iscorrect.

One idea associatedwith unified theories is supersymmetry.According to thishypothesis, there is an underlying symmetry between the fermions and thebosons, two families which are treated separately in the standard model. Insupersymmetric theories, every fermion has a boson ‘partner’ and vice versa.Quarkshavebosonicpartners called squarks,neutrinoshave sneutrinosand soon.Thephoton,aboson,hasafermionpartnercalledthephotino.ThepartneroftheHiggsbosonistheHiggsino,andsoon.Oneoftheinterestingpossibilitiesof

supersymmetryisthatatleastoneofthemyriadofparticlesthatoneexpectstoreveal themselves at very high energy might be stable. Could one of theseparticlesmakeupthedarkmatterthatseemstopervadetheUniverse?

Baryogenesis

It isclear that the ideaof symmetryplaysan important role inparticle theory.For example, the equations that describe electromagnetic interactions aresymmetricwhen it comes to electrical charge. If one changed all the positivechargesintonegativecharges,andviceversa,Maxwell’sequationsthatdescribeelectromagnetismwould still be correct. To put it another way, the choice ofassigning negative charge to electrons and positive charges to protons isarbitrary:itcouldhavebeendonetheotherwayaround,andnothingwouldbedifferent in the theory. This symmetry translates into the existence of aconservation law for charge; electrical charge can be neither created nordestroyed. It seems to make sense that our Universe should not have a netelectrical charge: there should be just as much positive charge as negativecharge,sothenetchargeisexpectedtobezero.Thisseemstobethecase.

The laws of Physics also seem to fail to distinguish betweenmatter and anti-matter. But we know that ordinary matter is much more common than anti-matter.Inparticular,weknowthatthenumberofbaryons(protonsandneutrons)exceeds the number of anti-baryons. Baryons actually carry an extra kind of‘charge’ called their baryon number B. The Universe carries a net baryonnumber.Likethenetelectriccharge,onewouldhavethoughtthatBshouldbeaconservedquantity.SoifB isnotzeronow, thereseemstobenoavoidingtheconclusionthat itcan’thavebeenzeroatanytimeinthepast.Theproblemofgeneratingthisasymmetry–theproblemofbaryogenesis–perplexedscientistsworkingontheBigBangtheoryforsomeconsiderabletime.

TheRussianphysicistAndreiSakharovin1967wasthefirsttoworkoutunderwhat conditions there could actually be a net baryon asymmetry and to showthat, in fact,baryonnumberneednotbeaconservedquantity.Hewasable toproduce an explanation in which the laws of Physics are indeed baryon-symmetric,andatearlytimestheUniversehadnonetbaryonnumber,butasitcooled a gradual preference for baryons over anti-baryons emerged.Hisworkwas astonishinglyprescient, because itwasperformed longbefore anyunified

theories of particle physics were constructed. He was able to suggest amechanismwhichcouldproduceasituationinwhichforeverythousandmillionanti-baryons in the early Universe, there were a thousand million and onebaryons.Whenabaryonandananti-baryoncollide,theyannihilateinapuffofelectromagnetic radiation. In Sakharov’s model, most of the baryons wouldencounteranti-baryons,andbeannihilatedinthisway.Wewouldeventuallybeleftwithauniversecontainingthousandsofmillionsofphotonsforeverybaryonthatsurvives.This isactuallythecaseinourUniverse.Thecosmicmicrowavebackground radiation contains billions of photons for every baryon. Theexplanation of this is a pleasing example of the interface between particlephysics and cosmology, but it is by nomeans themost dramatic. In the nextchapter,IwilldiscusstheideaofcosmicinflationaccordingtowhichsubatomicphysicsisthoughttoaffecttheentiregeometryoftheUniverse.

Chapter6What’sthematterwiththeUniverse?

Is theUniverse finite or infinite?Will theBigBang end in aBigCrunch? Isspacereallycurved?HowmuchmatteristhereintheUniverse?Andwhatformdoes this matter take? One would certainly hope that a successful scientificcosmology could provide answers to questions as basic as these. The answersdependcruciallyuponanumberknownasΩ(Omega).Astronomershavelonggrappled with the problem of how to measure Ω using observations of theUniverse around us, with only limited success. Dramatic progress in thedevelopmentandapplicationofnewtechnologynowsuggeststhepossibilitythatthevalueofΩmayfinallybepinneddownwithinthenextfewyears.Butthereisastinginthetale.ThemostrecentobservationssuggestthatΩdoesnot,afterall, hold all the answers. The issue of Ω is, however, not entirely anobservational one, because the precise value that this quantity takes holdsimportantcluesabouttheveryearlystagesoftheBigBang,andforthestructureofourUniverseonverylargescales.SowhyisΩsoimportantanditsvaluesoelusive?

ThequestforΩ

TounderstandtheroleofΩincosmology,itisfirstnecessarytorememberhowEinstein’s general theory of relativity relates geometrical properties of space-time(suchas itscurvatureandexpansion), to thephysicalpropertiesofmatter(such as its density and state of motion). As I explained in Chapter 3, theapplicationofthiscomplicatedtheoryincosmologyisgreatlysimplifiedbytheintroductionoftheCosmologicalPrinciple.Intheend,theevolutionoftheentireUniverse is governed by one relatively simple equation, now known as the

Friedmannequation.

TheFriedmannequationcanbethoughtofasexpressingthelawofconservationof energy for theUniverse as awhole.Energycomes inmanydifferent formsthroughout nature but only two relatively familiar forms are involved here.Amovingobject, suchasabullet, carriesa typeofenergycalledkinetic energy,which depends upon its mass and velocity. Obviously since the Universe isexpanding,andall thegalaxiesarerushingapart, theUniversecontainsagreatdealofkineticenergy.Theotherformofenergyispotentialenergy,whichisalittlemoredifficulttounderstand.Wheneveranobjectismovingandinteractingthrough some kind of force it can gain or lose potential energy. For example,imagine aweight tied on the end of a dangling piece of string. Thismakes asimplependulum.IfIraisetheweight,itgainspotentialenergybecauseIhavetoworkagainstgravitytoliftit.IfIthenreleasetheweightthependulumbeginsto swing. The weight then picks up kinetic energy and as it drops it losespotentialenergy.Energyistransferredbetweenthetwotypesinthisprocess,butthetotalenergyofthesystemisconserved.Theweightwillswingtothebottomofitsarc,whereithasnopotentialenergy,butitwillstillbemoving.Itwillinfactdescribeacompletecycle,returningeventuallytothetopofitsarcatwhichpoint itstops(instantaneously)beforestartinganotherswing.At the top, ithasnokineticenergybutmaximumpotential.Wherevertheweightis,theenergyofthissystemisconstant.Thisisthelawofconservationofenergy.

In cosmological terms, the kinetic energy depends crucially on the expansionrate or, in other words, upon the Hubble constant Ho. The potential energydependsonthedensityoftheUniverse,i.e.uponhowmuchmatterthereisperunit volume of the Universe. Unfortunately, this quantity is not known at allaccurately: it is even less certain than the value of theHubble constant. Ifweknew the mean density of matter and the value of Ho, however, we couldcalculate the total energy of the Universe. This would have to be constant intime, inaccordancewiththelawofconservationofenergy(or, in thiscontext,theFriedmannequation).

Setting aside the technical difficulties that arise when General Relativity isinvolved,wecannowdiscusstheevolutionoftheUniverseinbroadtermsusingfamiliarexamplesfromhigh-schoolphysics.Forinstance,considertheproblemoflaunchingavehiclefromEarthintospace.Herethemassresponsibleforthegravitationalpotentialenergyof thevehicle is theEarth.Thekineticenergyofthe vehicle is determined by the power of the rocket we use. If we give the

vehicleonlyamodestrocket,sothatitdoesn’tmoveveryquicklyatlaunch,thenthekineticenergyissmallandmaybeinsufficientfortherockettoescapefromtheattractionoftheEarth.Consequently,thevehiclegoesupsomewayandthencomesbackdownagain.Intermsofenergy,whathappensisthattherocketusesup itskineticenergy,givenexpensivelyat launch, topay theprice in termsofpotentialenergyforitsincreasedheight.Ifweuseabiggerrocket, itwouldgohigherbeforecrashingdowntotheground.Eventually,wewillfindarocketbigenoughtosupplythevehiclewithenoughenergyforittobuyitswaycompletelyout of the gravitational field of the Earth. The critical launch velocity here isusually called escape velocity: above the escape velocity, the rocket keeps ongoingforever;belowittherocketcomescrashingdownagain.

In thecosmologicalsetting thepicture issimilarbut thecriticalquantity isnotthe velocity of the rocket (which is analogous to the Hubble constant and istherefore known, at least in principle), but the mass of the Earth (or, in thecosmological case, the density of matter). It is therefore most useful to thinkaboutacriticaldensityofmatter,ratherthanacriticalvelocity.Iftherealdensityof matter exceeds the critical density, then the Universe will eventuallyrecollapse: its gravitational energy is sufficient to slow down, stop, and thenreverse the expansion. If the density is lower than this critical value, theUniversewill carry on expanding forever. The critical density turns out to beextremelysmall.ItalsodependsonHo,butisontheorderofonehydrogenatompercubicmetre.Mostmodernexperimentalphysicistswouldconsidermaterialwithsuchalowdensitytobeaverygoodexampleofavacuum!

16.TheFriedmannmodels.Aswellashavingvariousoptionsforcurvedspace,

the Friedmannmodels can also behave in different ways as they evolve withtime. IfΩ is greater than one then the expansionwill eventually stop and theUniversewillrecollapse.IfitislessthanonetheUniversewillexpandforever.PoisedbetweentheseistheflatUniversewithΩfinelytunedtobeexactlyunity.

Andnow,at last,wecan introduce thequantityΩ: it issimply theratioof theactual density of matter in the Universe to the critical value that marks thedividing line between eternal expansion and ultimate recollapse.Ω= 1marksthatdividingline:Ω1meansanever-expandingUniverse,andΩ>1indicatesonethatrecollapsesinthefuturetoaBigCrunch.WhatevertheprecisevalueofΩ,however, the effect of matter is always to slow down the expansion of theUniverse,sothatthesemodelsalwayspredictacosmicdeceleration,butmoreofthatshortly.Butthelong-termviabilityofthecosmologicalexpansionisnottheonly issuewhose resolution depends onΩ. These arguments based on simpleideas of energy resulting fromNewtonian physics are not thewhole story. InEinstein’s general theory of relativity, the total energy-density of materialdeterminestheglobalcurvatureofspace,asIdescribedinChapter3.Aspaceofnegative global curvature results inmodelswithΩ less than 1.Amodelwithnegative curvature is called an open universe model. A positively curved(closed) model pertains if Ω exceeds unity. In between, there is the classicBritish compromise universe, poised between eternal expansion and eventualrecollapse, which has Ω exactly equal to unity. This model also has a flatgeometryinwhichEuclid’stheoremsallapply.WhatareliefitwouldbeiftheUniversechosethissimplestofalloptions!

ThequantityΩdeterminesboth thegeometryof spaceoncosmological scalesandtheeventualfateoftheUniverse,butitisimportanttostressthatthevalueofΩisnotatallpredictedinthestandardBigBangmodel.Itmayseemtobeafairlyuselesskindof theory that is incapableofanswering thebasicquestionsthatrevolvearoundΩ,butinfactthatisanunfaircriticism.AsIhaveexplained,theBigBang isamodel, rather thana theory.Asamodel, it is self-consistentmathematically and compared to observations, but it is not complete. In thiscontext thismeans thatΩ is a ‘free’ parameter inmuch the sameway as theHubble constantHo.Toput it anotherway, themathematical equations of theBigBangtheorydescribetheevolutionoftheUniverse,butinordertocalculatea specific example we need to supply a set of initial conditions to act as astartingpoint.Sincethemathematicsonwhichthemodelisbasedbreakdownat

theverybeginning,wehavenowayoffixingtheinitialconditionstheoretically.TheFriedmannequation iswelldefinedwhatever thevaluesofΩandHo,butour Universe happens to have been set up with one particular numericalcombinationofthesequantities.Allwecando,therefore,istouseobservationaldatatomakeinferencesaboutthecosmologicalparameters:theycannot,atleastwiththeknowledgepresentlyavailableandwithintheframeworkofthestandardBig Bang, be deduced by reason alone. On the other hand, there is theopportunitytousepresent-daycosmologicalobservationstolearnabouttheveryearlyUniverse.

Thesearchfortwonumbers

The importance of determining the cosmological parameters was recognizedearlyoninthehistoryofcosmology.Indeed,thedistinguishedastronomerAllanSandage (formerly Hubble’s research student) once wrote a paper entitled‘Cosmology:TheSearch forTwoNumbers’.Twodecades later,westilldon’tknow the two numbers, and to understand why, we have to understand thedifferent kinds of observation that can inform us about Ω, and what kind ofresults theyhaveproduced.Therearemanydifferent typesofobservation,buttheycanbegroupedintofourmaincategories.

First,therearetheclassicalcosmologicaltests.Theideawiththesetestsistouseobservationsofverydistantobjectstomeasurethecurvatureofspace,ortherateatwhich the expansion of theUniverse is decelerating. The simplest of thesetests involves the comparison of the ages of astronomical objects (particularlystarsinglobularclustersystems)withtheagepredictedbycosmologicaltheory.IdiscussedthisinChapter4becauseiftheexpansionoftheUniversewerenotdecelerating, the predicted age dependsmuchmore sensitively on theHubbleconstantthanitdoesonΩ,andinanycasetheagesofoldstarsarenotknownwithanygreatconfidence, so this test isnotapowerfuldiagnosticofΩat themoment.OtherclassicaltestsinvolveusingthepropertiesofverydistantsourcestoprobedirectlytherateofdecelerationorthespatialgeometryoftheUniverse.Someof these techniqueswerepioneeredbyHubbleanddevelopedintoanartformbySandage.Theyfellintosomedisreputeinthe1960sand1970sbecauseit was then realized that not only was the Universe at large expanding, butobjects within it were evolving rapidly. Since one needs to probe very large

distancestomeasuretheveryslightgeometricaleffectsofspatialcurvature,oneisinevitablylookingatastronomicalobjectsastheywerewhentheirlightstartedoutonitsjourneytous.Thiscouldbeaverylongtimeagoindeed:morethan80per cent of the age of the Universe is commonplace in cosmologicalobservations. There is no guarantee that the brightness or size of the distantobjects being used had the same properties as nearby ones because of thepossibility that these properties change with time. Indeed the classicalcosmological tests are now largely used to study the evolution of properties,rather than to test fundamental aspects of cosmology. There is, however, oneimportant and recent exception.The use of supernovae explosions as standardlightsourceshasyieldedspectacularresultsthatseemtosuggesttheUniverseisnotdeceleratingatall.I’lltalkmoreabouttheseattheendofthechapter.

Next are arguments based on the theory of nucleosynthesis.As I explained inChapter 5, the agreement between observed elemental abundances and thepredictions of nuclear fusion calculations in the early Universe is one of themajor pillars of evidence supporting theBigBang theory. But this agreementonlyholds if thedensityofmatter isvery lowindeed:nomore thanafewpercentofthecriticaldensityrequiredtomakespaceflat.Thishasbeenknownformanyyears,andatfirstsightitseemstoprovideaverysimpleanswertoallthequestions I have posed. However, there is an important piece of small printattachedtothisargument.The‘fewpercent’limitonlyappliestomatterwhichcan participate in nuclear reactions. The Universe could be filled with abackgroundofsterileparticlesthatwereunabletoinfluencethesynthesisofthelightelements.Thekindofmatterthatinvolvesitselfinthingsnucleariscalledbaryonic matter and is made up of two basic particles, protons and neutrons.Particlephysicistshavesuggestedthatothertypesofparticlethanbaryoniconesmight have been produced in the seething cauldron of the early Universe. Atleastsomeoftheseparticlesmighthavesurviveduntilnow,andmaymakeupatleastsomeofthedarkmatter.AtleastsomeoftheconstituentsoftheUniversemay therefore comprise some form of exotic non-baryonic particle. Ordinarymatter, ofwhichwe aremade,maybebut a small contaminating stainon thevast bulk of cosmicmaterialwhose nature is yet to be determined. This addsanotherdimensiontotheCopernicanPrinciple:notonlyarewenolongeratthecentreof thecosmos,we’renotevenmadefromthesamestuffasmostof theUniverse.

The third category of evidence is based on astrophysical arguments. Thedifference between these arguments and the intrinsically cosmological

measurementsdiscussedaboveisthattheylookatindividualobjectsratherthanthepropertiesofthespacebetweenthem.Ineffect,oneistryingtodeterminethedensity of theUniverse byweighing its constituent elements one by one. Forexample,onecanattempt touse the internaldynamicsofgalaxies toworkouttheirmasses by assuming that the rotation of a galactic disk ismaintained bygravity in much the same way as the motion of the Earth around the Sun isgoverned by the Sun’s gravity. It is possible to calculate themass of the SunfromthevelocityoftheEarthinitsorbit,andasimilarcalculationcanbedoneforgalaxies:theorbitalspeedsofthestarsingalaxiesisdeterminedbythetotalmass of the galaxy pulling on them. The principle can also be extended toclusters of galaxies, and systems of even larger size than this. Theseinvestigations overwhelmingly point to the existence of muchmore matter ingalaxiesthanoneseesthereintheformofstarslikeoursun.Thisisthefamousdark matter we can’t see but whose existence we infer from its gravitationaleffects.

Rich clusters of galaxies – systems more than a million light years acrossconsistingofhugeagglomerationsofgalaxies–alsocontainmorematterthanisassociatedwith the individualgalaxies in them.Theexactamountofmatter isunclear,butthereisverystrongevidencethatthereisenoughmatterintherichcluster systems to suggest thatOmega is certainly as big as 0.1, and possiblyeven larger than 0.3. Tentative evidence from the dynamics of even largerstructures – superclusters of clusters that are tens ofmillions of light years insize–suggeststhere

17. TheComa cluster. This is an example of a rich cluster of galaxies.Asidefromtheoddstar(suchastheonetotherightoftheframe),theobjectsinthispictureareallgalaxiescontainedwithinagiantcluster.Suchenormousclustersare fairly rare but contain phenomenal amounts of mass, up to100,000,000,000,000timesthemassoftheSun.

18. Coma in X-rays. As well as the many hundreds of galaxies seen in theprevious picture, clusters such asComa also contain very hot gas that can beseenintheX-radiationitemits.ThispicturewastakenbytheROSATsatellite.

may be even more dark matter lurking in the space between clusters. Thesedynamicalargumentshavealsomorerecentlybeentestedandconfirmedagainstindependentobservationsof thegravitational lensingproducedbyclusters,andby measurements of the properties of the very hot X-ray-emitting gas thatpervadesthem.Intriguingly,thefractionofbaryonicmatterinclusterscomparedto their total mass seems much larger than the global value allowed bynucleosynthesis if there is a critical density of matter overall. This so-calledbaryoncatastrophemeansthateithertheoveralldensityofmatterismuchlowerthan the critical value or some unknown process may have concentratedbaryonicmatterinclusters.

Finally, we have clues based on attempts to understand the origin ofcosmological structure: how the considerable lumpiness and irregularityof theUniverse can have developedwithin a Universe that is required to be largelysmoothby theCosmologicalPrinciple.The ideabehindhow this is thought tohappenintheBigBangmodelsisdiscussedinmoredetail inthenextchapter.The basic principles are, I believe, relatively well understood. The details,however, turn out to be incredibly complicated and prone to all kinds of

uncertaintyandbias.ModelscanandhavebeenconstructedwhichseemtofitalltheavailabledatawithΩveryclose tounity.Others cando the same,withΩmuch less than this. This may sound a bit depressing, but this kind of studyprobably ultimately holds the key to a successful determination ofΩ. Ifmoredetailed measurements of the features in the microwave background can bemade, then the properties of these features will tell us immediately what thedensity ofmattermust be.And, as a bonus, itwill also determine theHubbleconstant,bypassingallthetediousbusinessofthecosmologicaldistanceladder.Wecanonlyhope that thesatellitesplanned todo this,MAP(NASA)and thePlanck Surveyor (ESA), will fly successfully in the next few years. Recentballoonexperimentshave shown that this appears tobe feasible, but I’ll leavethistoChapter7todiscussfurther.

19. Gravitational lensing. Rich clusters can be weighed by observing thedistortionoflightfrombackgroundgalaxiesasitpassesthroughthecluster.InthisbeautifulexampleoftheclusterAbell2218lightfrombackgroundsourcesisfocused into a complicated pattern of arcs as the cluster acts as a giant lens.Thesefeaturesrevealtheamountofmasscontainedwithinthecluster.

We can summarize the status of the evidence by suggesting that the vastmajorityofcosmologistsprobablyacceptthatthevalueofΩcannotbesmallerthan 0.2. Even this minimal value requires that most of the matter in theUniverse is dark. It alsomeans that at least somemust not be in the form ofprotons and neutrons (baryons), which is where most of the mass resides inmaterialwithwhichwearefamiliarineverydayexperience.Inotherwordstheremust be non-baryonic dark matter. Many cosmologists favour a value of Ωaround 0.3, which seems to be consistent with most of the observationalevidence.Somehaveclaimedthat theevidencesupportsavalueof thedensityclose to the critical value, so thatΩ can be very close to unity.This is partlybecause of the accumulating astronomical evidence for dark matter, but also

because of the theoretical realization that non-baryonic matter might beproducedatveryhighenergiesintheBigBang.

Thecosmictightrope

The considerable controversy surrounding Ω is only partly caused bydisagreements resulting from the difficulty of assessing the reliability andaccuracy of (sometimes conflicting) observational evidence. The most vocalarguments in favour of a high value for Ω (i.e. close to unity) are based ontheoretical, rather than observational, arguments. One might be inclined todismiss such arguments asmereprejudice, but theyhave their roots in a deepmysteryinherent tothestandardBigBangtheoryandwhichcosmologists takeveryseriouslyindeed.

To understand the nature of thismystery, imagine you are standing outside asealedroom.Thecontentsoftheroomarehiddenfromyou,exceptforasmallwindowcoveredbyalittledoor.Youaretoldthatyoucanopenthedooratanytime youwish, but only once, and only briefly.You are told that the room isbare,exceptforatightropesuspendedinthemiddleabouttwometresintheair,and a man who, at some indeterminate time in the past began to walk thetightrope.Youknowalsothatifthemanfalls,hewillstayontheflooruntilyouopenthedoor.Ifhedoesn’tfall,hewillcontinuewalkingthetightropeuntilyoulookin.

What do you expect to seewhenyouopen the door?Whether you expect themantobeontheropeoronthegrounddependsoninformationyoudon’thave.Ifheisacircusartist,hemightwellbeabletowalktoandfroalongtheropeforhoursonendwithout falling. If,on theotherhand,hewerenota specialist inthis area (likemostofus), his stayon the ropewouldbe relativelybrief.Onething,however,isobvious.Ifthemanfalls,itwilltakehimaveryshorttimetofall fromtherope to thefloor.Youwouldbeverysurprised, therefore, ifyourpeep through the window happened to catch the man in transit from rope toground.Itisreasonable,onthegroundsofwhatweknowaboutthissituation,toexpect themantobeeitherontheropeoronthegroundwhenwelook,but ifyouseehiminmid-tumbleyouwouldconcludethatsomethingfishyisgoingon.

This may not seem to have much to do with Ω, but the analogy becomes

apparentwiththerealizationthatΩdoesnothaveaconstantvalueastimegoesby.InthestandardFriedmannmodels,Ωevolvesanddoessoinaverypeculiarway.AttimesarbitrarilyclosetotheBigBang,thesemodelsarealldescribedbyavalueofΩarbitrarilyclosetounity.Toputthisanotherway,lookatFigure16.Regardlessofthebehaviouratlatetimes,allthreecurvesshowngetcloserandcloser together near the beginning and, in particular, they approach the ‘flatUniverse’line.Astimepasses,modelswithΩjustalittlebitgreaterthanunityintheearlystagesdeveloplargerandlargervaluesofΩ,withvaluesfargreaterthanunitywhenrecollapsebegins.UniversesthatstartoutwithvaluesofΩjustlessthanunityeventuallyexpandmuchfasterthantheflatmodel,andthenhavevaluesofΩveryclosetozero.Inthelattercase,whichisprobablymorerelevantgiventhemanyindicationsthatΩislessthanunity,thetransitionfromΩnearunity,toΩnearzeroisveryrapid.

Nowwecanseetheproblem.IfΩis,say,0.3, thenintheveryearlystagesofcosmic history it was very close to unity, but less than this value by a tinyamount. In fact, it really is a tiny amount indeed. At the Planck time, forexample(i.e.10–43secondsaftertheBigBang),Ωhadtodifferfromunityonlyin the 60th decimal place. As time went by, Ω hovered close to the criticaldensity state, only beginning to diverge rapidly in the recent past. In the verynearfutureitwillbeextremelyclosetozero.Butnow,itisasifwecaughtthetightropewalkerrightinthemiddleofhisfall.Thisseemsverysurprising,toputitmildly.

Thisparadoxhasbecomeknownas theCosmologicalFlatnessProblem,and itarisesfromtheincompletenessofthestandardBigBangtheory.Thatitissuchabigproblemconvincedmany scientists that it needed a big solution.Theonlyway that seemed likely to resolve theconundrumwas thatourUniverse reallyhadtobeaprofessionalcircusartist, tostretchthemetaphortobreakingpoint.Obviously,Ωisnotclosetozero,aswehavestrongevidenceofalowerlimittoitsvaluearound20percent.This rulesout theman-on-the-groundalternative.The argument then goes thatΩmust be equal to unity very closely, and thatsomethingmusthavehappenedinprimordialtimestosingleoutthisvalueveryaccurately.

Inflationandflatness

The happening that did this is claimed to be cosmological inflation, aspeculation,originallymadebyAlanGuthin1981,abouttheveryearlystagesoftheBigBangmodel.Inflationinvolvesacuriouschangeinthepropertiesofmatteratveryhighenergiesknownasaphasetransition.

Wehavealreadycomeacrossanexampleofaphase transition.Oneoccurs inthe standard model about one-millionth of a second of the Big Bang, and itinvolves the interactions between quarks. At low temperatures, quarks areconfined in hadrons, whereas at higher temperatures they form a quark-gluonplasma. Inbetween, there isaphase transition. Inmanyunified theories, therecanbemanydifferentphasetransitionsatevenhighertemperaturesallmarkingchangesintheformandpropertiesofmatterandenergyintheUniverse.Undercertaincircumstancesaphasetransitioncanbeaccompaniedbytheappearanceofenergyinemptyspace;thisiscalledthevacuumenergy.Ifthishappens,theUniverse begins to expand much more rapidly than it does in the standardFriedmannmodels.Thisiscosmicinflation.

Inflation has had a great impact on cosmological theory over the last twentyyears. In this context, the most important thing about it is that the phase ofextravagantexpansion–whichisveryshort-lived–actuallyreversesthewayΩwould otherwise change with time. Ω is driven hard towards unity wheninflationstarts,ratherthandriftingawayfromitasitdoesinthecasesdescribedabove. Inflation acts like a safety harness, pushing our tightrope walker backonto the wire whenever he seems like falling. An easy way of understandinghowthishappensistoexploittheconnectionIhaveestablishedalreadybetweenthe value of Ω and the curvature of space. Remember that a flat spacecorrespondstoacriticaldensity,andthereforetoavalueofΩequaltounity.IfΩdiffersfromthismagicvaluethenspacemaybecurved.Ifonetakesahighlycurvedballoonandblows itup toanenormoussize, say thesizeof theEarth,thenitssurfacewillappearflat.Ininflationarycosmology,theballoonstartsoffa tiny fraction of a centimetre across and ends up larger than the entireobservableUniverse.Ifthetheoryofinflationiscorrect,thenweshouldexpecttobelivinginaUniversewhichisveryflatindeed.Ontheotherhand,evenifΩwere to turnout tobeveryclose tounity, thatwouldn’tnecessarilyprove thatinflation happened. Some other mechanism, perhaps associated with quantumgravitationalphenomena,mighthavetrainedourUniversetowalkthetightrope.These theoretical ideas are extremely important, but they cannot themselvesdecide the issue.Ultimately,whether theorists like itornot,wehave toacceptthat cosmology has become an empirical science. We may have theoretical

grounds for suspecting thatΩ should be very close to unity, but observationsmustprevailintheend.

Thesting

Thequestionthatemergesfromallthisisthatif,asseemstentativelytobethecase,Ωissignificantlysmallerthanunity,dowehavetoabandoninflation?Theanswer is ‘notnecessarily’.Forone thing,somemodelsof inflationhavebeenconstructed that can produce an open, negatively curved Universe. Manycosmologists don’t like thesemodels,which do appear rather contrived.Moreimportantly, there are now indications that the connection betweenΩ and thegeometryofspacemaybelessstraightforwardthanhaspreviouslybeenthought.Aftermanyyearsinthewilderness,theclassicalcosmologicaltestsImentionedearlier have now staged a dramatic comeback. Two international teams ofastronomershavebeenstudyingthepropertiesofaparticulartypeofexplodingstar,aTypeIaSupernova.

Asupernovaexplosionmarksthedramaticendpointofthelifeofamassivestar.Supernovae are among themost spectacular phenomena known to astronomy.They aremore than a billion times brighter than the Sun and can outshine anentire galaxy for several weeks. Supernovae have been observed throughoutrecordedhistory.A supernovaobserved and recorded in1054gave rise to theCrabNebula,acloudofdustanddebrisinsidewhichliesarapidlyrotatingstarcalledapulsar.ThegreatDanishastronomerTychoBraheobservedasupernovain1572.Thelastsucheventtobeseeninourgalaxywasrecordedin1604andwasknownasKepler’sstar.AlthoughtheaveragerateoftheseexplosionsintheMilky Way appears to be one or two every century or so, based on ancientrecords, none has been observed for nearly 400 years. In 1987, however, asupernova did explode in the LargeMagellanic Cloud and was visible to thenakedeye.

There are two distinct kinds of supernova, labelled Type I and Type II.Spectroscopic measurements reveal the presence of hydrogen in the Type IIsupernovae, but this is absent in the Type I versions. Type II supernovae arethought tooriginatedirectly from theexplosionsofmassivestars inwhich thecoreofthestarcollapsestoakindofdeadrelic,whiletheoutershellisejectedinto space. The final state of this explosionwould be a neutron star or black

hole.TypeIIsupernovamayresultfromthecollapseofstarsofdifferentmass,so there is considerable variation in their properties from one to another. TheTypeIsupernovaearefurthersubdividedintoTypeIa,IbandIc,dependingondetails of the shape of their spectra.TheType Ia supernovae are of particularinterest.Thesehaveveryuniformpeakluminosities,forthereasonthattheyarethoughttobetheresultofthesamekindofexplosion.Theusualmodelfortheseeventsisthatawhitedwarfstarisgainingmassbyaccretionfromacompanion.When the mass of the white dwarf exceeds a critical mass called theChandrasekhar mass (about 1.4 times the mass of the Sun), its outer partsexplodewhileitscentralpartscollapse.Sincethemassinvolvedintheexplosionisalwaysveryclose to thiscriticalvalue, theseobjectsareexpectedalways toresult in the liberation of the same amount of energy. The regularity of theirpropertiesmeansthatTypeIasupernovaeareverypromisingobjectswithwhichtoperform testsof thecurvatureof space-timeand thedeceleration rateof theUniverse.

New technology has enabled astronomers to search (and find) Type Ia ingalaxieswithredshiftsaroundone.(RememberthatthismeansthattheUniversehas expanded by a factor of two while light has been travelling from thesupernova to us.)Comparing the observed brightness of the distant supernovawithnearbyonescangiveanestimateofhowmuchfurtherawaytheyare.This,inturn,tellsushowmuchtheUniversehasbeenslowingdowninthetimetakenforthelighttoreachus.Thetroubleisthatthesesupernovaearefainterthantheyshouldbeif theUniverseisslowingdown.TheUniverseisnotdeceleratingatall,butspeedingup.

This observation strikes at the heart of the standard description of cosmologyembodiedintheFriedmannequations.Allthesemodelsshouldbedecelerating.Even themembersof theFriedmannfamilywith lowΩ,whosedeceleration isonly slight owing to their low density, should not be speeding up. And themodels with critical density apparently favoured by inflation should undergoheavydeceleration.Whathasgonewrong?

Einstein’sbiggestwonder?

The supernova observations I’ve been talking about are still controversial, buttheycertainlyseemtoindicatethatadramaticchangeincosmologicaltheoryis

needed. On the other hand, there is an off-the-shelf remedy for this bug thatdatesfromEinsteinhimself.InChapter3ImentionedhowEinsteinalteredhisoriginaltheoryofgravitationbyintroducingacosmologicalconstant.Hisreasonfordoingthis,anacthelaterregretted,wasthathewantedtomakeatheorythatcoulddescribeastatic(i.e.non-expanding)universe.Hiscosmologicalconstantalteredthelawofgravitytopreventspacefromeitherexpandingorcontracting.Appliedin themoderncontext, thecosmologicalconstantcanbeintroducedtomakethelawofgravityrepulsiveonlargescales.Ifthisisdone,thetendencyofthegravitationalattractionofmattertoslowdowntheUniverseisoverwhelmedbyacosmicrepulsionthatcausesittospeedup.

Thiscureofcourserequiresonetoacceptthatthecosmologicalconstantwasn’ta bad idea in the first place. But modern theory also gives us a newunderstanding of how this can happen. In Einstein’s original theory, thecosmologicalconstantappearedinthemathematicalequationsdescribinggravityandspace-timecurvature.Itwasindeedamodificationofthelawofgravity.Buthecouldjustaseasilyhavewrittenthistermontheothersideofhisequations,in the part of the theory that describes matter. Over on the other side ofEinstein’s equations, his infamous cosmological constant appears as a termdescribing the energy density of the vacuum.A vacuum that has energymaysound strange, butwehave come across it before in this chapter. It is exactlywhatisneededtocauseinflation.

Intheearlyversionsofcosmicinflationtheory,thevacuumenergyliberatedbya primordial phase transition disappears after the transient period of hyper-expansionisover.Butmaybeasmallamountofthisenergysurviveduntilnowanditisthisenergythathasmadegravitypushinsteadofpull.Theideathatthisvacuumenergymaybecausingtheaccelerationalsoallowsustoreconcile thetheoryof inflationwith the evidence thatΩmaybe significantly less than theunitvalueitwouldhavetohaveifspacewereflat.Whilethevacuumenergyisperverseinthatitmakesgravitypushratherthanpull,itdoesatleastcurvespacein the same way that ordinary matter does. If we have a Universe with bothmatterandvacuumenergythenwecanhaveflatspacewithoutthedecelerationthatisrequiredinanordinaryFriedmannmodel.

Westilldon’treallyknowforsurewhethertheUniverseisaccelerating,whetherthere is avacuumenergy,orwhatprecisely is thevalueofΩ.But these ideashave provoked intense activity over the last few years in both theory andexperiment.Andthere isanewgenerationofmeasurementscomingalongthat

could, if they work, answer all these questions. I’ll discuss these in the nextchapter.

Chapter7Cosmicstructures

Galaxiesare thebasicbuildingblocksof theUniverse.Theyarenot,however,thelargeststructuresonecansee.Theytendnottobeisolated,butliketobandtogether rather like people. The term used to describe the way galaxies aredistributed over cosmological distances is large-scale structure. The origin ofthis structure is one of the hot topics of modern cosmology but, beforeexplaining why this is so, it is first necessary to describe what the structureactuallyis.

Patternsinspace

The distribution of matter on large scales is usually determined by means ofspectroscopic surveys that use Hubble’s Law to estimate the distances togalaxies from their redshifts. The existence of structure was known formanyyearsbeforeredshiftsurveysbecamepracticable.Thedistributionofgalaxiesontheskyishighlynon-uniform,ascanbeseeninthefirstlargesystematicsurveyofgalaxypositionswhichresultedintheLickMap.Butimpressivethoughthismap undoubtedly is, one cannot be sure if the structures seen in it are real,physicalstructuresor justchanceprojectioneffects.Afterall,weall recognizetheconstellations,butthesearenotphysicalassociations.Thestarsinthemlieatvery different distances from the Sun. For this reason, the principal tool ofcosmographyhasbecometheredshiftsurvey.

20.TheAndromedaNebula.ThenearestlargespiralgalaxytotheMilkyWay,Andromeda is a good example of its type. Not all galaxies are spiral; richclusterslikeComacontainmainlyellipticalgalaxieswithnospiralarms.

A famous example of this approach is the Harvard-Smithsonian Center forAstrophysics(CfA)survey,whichpublisheditsfirstresultsin1986.Thiswasasurveyoftheredshiftsof1,061galaxiesfoundinanarrowstripontheskyintheoriginalPalomarSkySurveypublished in 1961.This surveyhas subsequentlybeenextendedtoseveralmorestripsbythesameteam.Untilthe1990sredshiftsurveyswereslowandlaboriousbecauseitwasnecessarytopointatelescopeateachgalaxyinturn,takeaspectrum,calculatetheredshiftandthenmovetothenextgalaxy.Toacquireseveralthousandsofredshiftstookmonthsoftelescopetime,which,becauseofthecompetitionforresources,wouldusuallybespreadoverseveralyears.Morerecentlytheinventionofmulti-fibredevicesonwide-field telescopeshas allowedastronomers to capture asmanyas400 spectra inonepointingofthetelescope.AmongthelatestgenerationofredshiftsurveysisonecalledtheTwo-DegreeField(2dF)survey,runbytheUnitedKingdomandAustralia using the Anglo-Australian Telescope. This will eventuallymap thepositionsofaround250,000galaxies.

21. The Lick Map. Produced by meticulous eyeball counting of galaxies onsurveyplates,theLickMapdisplaysthedistributionofaboutamilliongalaxiesoverthesky.Thepatternoffilamentsandclustersisimpressive;thedenseroundlumpnearthecentreistheComacluster.

Thegeneraltermusedtodescribeaphysicalaggregationofmanygalaxiesisaclusterofgalaxies,orgalaxycluster.Clusterscanbesystemsofgreatlyvaryingsizeandrichness.Forexample,ourgalaxy,theMilkyWay,isamemberoftheso-calledLocalGroupofgalaxies,whichisarathersmallclusterofgalaxiesofwhichtheonlyotherlargememberistheAndromedagalaxy(M31).Attheotherextreme, there are the so-called rich clusters of galaxies, also known asAbellclusters,whichcontainmanyhundredsoreventhousandsofgalaxiesinaregionjustafewmillionlightyearsacross:prominentnearbyexamplesofsuchentitiesaretheVirgoandComaclusters.Inbetweenthesetwoextremes,galaxiesappearto be distributed in systems of varying density in a roughly fractal (orhierarchical) manner. The densest Abell clusters are clearly collapsed objectsheld together in equilibriumby their own self-gravity.The less rich andmorespatiallyextendedsystemsmaynotbeboundinthisway,butmaysimplyreflect

ageneralstatisticaltendencyofgalaxiestoclumptogether.

Individual galaxy clusters are still not the largest structures to be seen. Thedistributionofgalaxiesonscales larger thanaround30millionlightyearsalsoreveals awealth of complexity.Recent observational surveys have shown thatgalaxies are not simply distributed in quasi-spherical ‘blobs’, like the Abellclusters, but also sometimes lie in extended quasi-linear structures calledfilaments, or flattened sheet-like structures such as theGreat Wall. This is aroughly two-dimensional concentration of galaxies, discovered in 1988 byastronomersfromtheHarvard-SmithsonianCenterforAstrophysics.TheGreatWallisatleast200millionlightyearsby600millionlightyearsinsize,butislessthan20millionlightyearsthick.Itcontainsmanythousandsofgalaxiesandhas a mass of at least 1016 solar masses. The rich clusters themselves areclustered into enormous loosely bound agglomerations called superclusters.Manyareknown,containinganythingfromaroundtenrichclusterstomorethanfifty. The most prominent known supercluster is called the Shapleyconcentration,whilethenearestistheLocalSupercluster,centredontheVirgoclustermentioned above, a flattened structure in the plane ofwhich theLocalGroup ismoving. Superclusters are knownwith sizes as large as 300millionlightyears,containingasmuchas1017solarmassesofmaterial.

Thesestructuresarecomplementedbyvastnearlyemptyregions,manyofwhichappeartoberoughlyspherical.These‘voids’containverymanyfewergalaxiesthanaverage,orevennogalaxiesatall.Voidswith

22. The 2dF galaxy redshift survey. This survey,which is still in progress, isplannedtomeasuretheredshiftsofaround250,000galaxies.Althoughpartsofthesurveyarenotfinished,resultinginmissingpiecesofthemap,onecanseetheemergenceof a complexnetworkof structures extendingout tobillionsoflightyearsfromus.

densitylessthan10percentoftheaveragedensityonscalesofupto200millionlightyearshavebeendetected in large-scale redshift surveys.Theexistenceoflarge voids is not surprising, given the existence of clusters of galaxies andsuperclusters on very large scales, because it is necessary to create regions oflessthanaveragedensityfortheretoberegionsofgreaterthanaveragedensity.

Theimpressiononehaswhenlookingatmapsoflarge-scalestructureisthatofavast cosmic ‘web’, a complex network of intersecting chains and sheets. Buthow did this complexity arise? The Big Bang model is predicated on theassumption that theUniverse issmoothandfeatureless, i.e. that itconforms totheCosmologicalPrinciple.Fortunatelythestructuredoesindeedseemtopeteroutonscaleslargerthanthescaleofthecosmicmesh.Thisisalsoconfirmedbyobservations of the cosmic microwave background, which comes to us aftertravellingabout15billion lightyears fromtheearlyUniverse.Themicrowavebackground is almost uniform on the sky, consistent with the Cosmological

Principle.Almost,thatis,butnotquite.

Structureformation

In 1992, the COBE satellite deployed its sensitive detectors to the task ofdetecting and mapping any variation in the temperature of the microwavebackground on the sky. At its discovery in 1965 the microwave backgroundseemed tobe isotropicon the sky.Later itwas found that it had a large-scalevariationacrosstheskyofaboutonepartinathousandofthetemperature.ThisisnowknowntobeaDopplereffect,causedbytheEarth’smotionthroughtheradiationfieldleftoverfromtheBigBang.Theskylooksslightlywarmerinthedirection we are heading, and slightly cooler in the direction we are comingfrom.Butasidefromthis‘dipole’variation(asitiscalled),theradiationseemedtobecomingequallyfromalldirections.Buttheoristshadsuspectedforalongtimethatthereshouldbestructureinthemicrowavebackground,intheformofaripplypatternofhotandcoldsplotches.ItwasthesethatCOBEfound,andinsodoing,causednewspaperheadlinesaroundtheworld.

So why is the microwave background not smooth after all? The answer isintimately connected to the origin of large-scale structure and, as ever incosmology,gravityprovidestheconnection.

Friedmann’smodelsprovideimportant insights intohowthebulkpropertiesoftheUniversechangewithtime.Buttheyareunrealisticbecausetheydescribeanidealizedworldthatisperfectlysmoothandblemish-free.AUniversethatstartsout like thatwill remainperfect forever. Ina realisticsituation,however, thereare always imperfections. Some regions may be slightly denser than average,somemorerarefied.HowdoesaslightlylumpyUniversebehave?Theanswerisdramatically different to the idealized case. A piece of the Universe that isdenserthanaverageexertsastrongergravitationalpullonitssurroundingsthanaverage.Itwill therefore tendtosuckmaterial in,depletingitsneighbourhood.Intheprocessitgetsevendenserrelativetotheaverage,andpullsstillharder.Theeffectisarunawaygrowthoflumpinesscalledthe‘gravitationalinstability’.Eventually strongly bound lumps form and begin to collect into filaments andsheets resembling those seen in maps of cosmic structure. Only very slightfluctuationsareneededtokicktheprocessoff,butgravityactslikeapowerfulamplifier transformingminute initial ripples into huge fluctuations in density.

Wecanmaptheendproductusinggalaxysurveys;weseetheinitialinputintheCOBE map. We even have a good theory of how the initial fluctuationsimprinted;cosmicinflationproducesquantumfluctuations.

Thebasicpictureofhowstructureformshasbeenaroundformanyyears,butitis hard to turn this into detailed predictive calculations because of thecomplicatedbehaviourofgravity.ImentionedinChapter3thatevenNewton’slawsofmotionaredifficult tosolvewithout simplifyingsymmetry. In the latestagesofgravitational instability, thereisnosuchsimplification.Everythinginthe Universe pulls on everything else; it is necessary to keep track of all theforcesactingeverywhereandoneverything.Thesumsinvolvedarejusttoohardtobesolvedwithpencilandpaper.

23. The COBE ripples. In 1992 the Cosmic Background Explorer (COBE)satellite measured slight fluctuations of about one part in 100,000 of thetemperatureofthecosmicmicrowavebackgroundonthesky.These‘ripples’arethoughttobetheseedsfromwhichgalaxiesandlarge-scalestructuregrew.

Duringthe1980s,however,massivecomputerscameonthescene,andprogressin the field accelerated. It became obvious that gravity could form cosmicstructurebutinorderforittodothejobeffectivelytherewouldhavetobequitea lot of mass in the Universe. Because only a relatively small amount of‘normal’matter is allowed by primordial nucleosynthesis arguments, theoristsassumedtheUniversetobedominatedbysomeformofexoticdarkmatterthatdoes not involve itself in nuclear reactions. Simulations showed that the bestformofmatterforthiswas‘cold’darkmatter.Ifthedarkmatterwere‘hot’thenitwouldbemovingtooquicklytoformclumpsoftherightsize.

Eventually, after many years of computer time, a picture emerged in whichcosmicstructurearisesinabottom-upfashion.First,smallclumpsofdarkmatterform. These building blocks then coalesce into larger units, which thenthemselvescoalesce,andsoon.Eventuallyobjectsthesizeofgalaxiesform.Gas(whichismadeofbaryonicmaterial)fallsin,starsform,andwehavegalaxies.Thegalaxiescontinuethehierarchicalgrowthofstructurebyclusteringinchainsandsheets.Inthispicture,structureevolvesrapidlywithtime(or,equivalently,withredshift).

24.TheHubbledeepfield.MadebypointingtheHubbleSpaceTelescopeatablankpieceofsky,thisimageshowsawonderfularrayofdistantfaintgalaxies.Someoftheseobjectsareatsuchenormousdistancesthatlighthastakenmorethan90per cent of the ageof theUniverse to reachus.Wecan therefore seegalaxyevolutionhappening.

Theideaofcolddarkmatterhasbeenverysuccessful,butthisprogrammeisfarfrom complete. It is still not known howmuch darkmatter there is, norwhat

form it takes. The detailed problem of how galaxies form is also unsolvedbecauseof thecomplexhydrodynamical and radiativeprocesses involvedwiththemotionofgasandtheformationofstars.Butnowthisfieldisnotjustabouttheoryandsimulations.Breakthroughsinobservationaltechnology,suchastheHubbleSpaceTelescope,nowallowustoseegalaxiesathighredshiftandthusstudypreciselyhowtheirpropertiesanddistributioninspacehaschangedwithtime.Withthenextgenerationofhugeredshiftsurveyswewillhaveenormouslydetailedinformationabout thepatternthatgalaxies traceout inspace.This tooholds clues as to howmuch dark matter there is, and precisely how galaxiesformed. But the final resolution of this problem is likely to come not fromobservationsoftheendproductofthegravitationalinstabilityprocessbutatitsbeginning.

Thesoundofcreation

TheCOBEsatellite representedanenormousadvance in thestudyof structureformation, but in many ways this experiment was very limited. The mostimportant shortcoming of COBE was that it lacked the ability to resolve thedetailedstructureof the ripples in themicrowavebackground. In factCOBE’sangular resolution was only about ten degrees, which is very crude byastronomical standards.The fullMoon, for comparison, is about half a degreeacross.Itisinthefinestructureofthemicrowaveskythatcosmologistshopetofindtheanswerstomanyoutstandingquestions.

TheripplesintheearlyUniversewereproducedbyakindofsoundwave.WhentheUniversewas very hot,with a temperature of several thousand degrees, itwasringingwithsoundwavestravellingbackwardsandforwards.ThesurfaceoftheSunisatasimilartemperatureandisvibratinginasimilarway.BecauseofitspoorresolutionCOBEwasabletodetectonlythoseripplesthathaveaverylongwavelength.Theserepresentsoundwavesofverylowpitch,thebassnotesofcreation.Theinformationcontainedinthesewavesisimportantbutnotverydetailed;theirsoundisratherdull.

25. Simulation of structure formation. Starting from almost smooth initialconditions,modernsupercomputerscanbeusedtoevolveasimulatedchunkofthe Universe forward in time. In this example, performed by the VirgoConsortium,wecanseehierarchicalclusteringdevelopastheUniverseexpandsbyafactorof4.Thedenseknotsseeninthelastframeformgalaxiesandgalaxyclusters,while the filamentary structure is strongly reminiscent of that seen inthegalaxysurveys.

Ontheotherhand,theUniverseshouldalsoproducesoundofhigherpitchandthisismuchmoreinteresting.Soundwavestravelwithaparticularspeed.Inair,for example, this is around 300metres per second. In the early Universe thesound speed ismuch greater, approaching the speed of light. By the time themicrowavebackgroundisproducedtheUniverseisabout300,000yearsold.Inthe time up to then since theBigBang,which is presumablywhen the sound

waveswereexcitedinthefirstplace,theycanhavetravelledonlyabout300,000lightyears.Oscillationswiththiswavelengthproduceacharacteristic‘note’,likethe fundamental tone of a musical instrument. It is no coincidence thatsuperclusters of galaxies are roughly of this size; they result from thisresoundingcosmicfanfare.

The characteristicwavelength of the earlyUniverse should reveal itself in thepatternofhotandcoldspotsonthemicrowavesky,butbecausethewavelengthisquiteshortitappearsasamuchfinerscalethancanberesolvedbyCOBE.Infact,theangularsizeofthespotsitproducesisaroundonedegree.SinceCOBE,therefore,therehasbeenaracetodevelopinstrumentscapableofdetectingnotjust the fundamental tone of theUniverse but also its higher harmonics.By adetailed analysis of the sound of creation, it is hoped to answermany of themajor questions facing modern cosmology. The spectrum of sound containsinformation about how much mass there is, whether there is a cosmologicalconstant,whattheHubbleconstantis,whetherspaceiscurved,andperhapsevenwhetherinflationhappenedornot.

Twomajor experiments, theNASA-ledMAPmission to be launched in 2001andtheEuropeanSpaceAgency’sPlanckSurveyortobelaunchedafewyearslater,willmakedetailedmapsofthepatternofripplesontheskywithveryhighresolution. If the interpretation of these structures is correct, we should havedefiniteanswersverysoon.Thesenseofanticipationispalpable.

Inthemeantime,thereareverystronghintsastohowthingswillpanout.Twoimportant balloon-borne experiments, BOOMERANG and MAXIMA, havemappedlittlebitsoftheskywithonlyslightlypoorerresolutionthanMAPandPlanckwill.Theseexperimentshavenotyieldeddefinitiveanswers,buttheydoindicate that thegeometryof theUniverse is flat.Theargument is simple.Weknow the characteristic wavelength of the sounds producing the measuredfeatures.We know how far away these waves are observed (about 15 billionlightyears).Wecan thereforeworkoutwhatangle theyshouldoccupyon theskyiftheUniverseisflat.IftheUniverseisopentheanglewillbesmallerthanitwouldbeinaflatUniverse;ifitisclosedtheanglewillbelarger.Theresultsimply flatness. Together with the acceleration I talked about in the previouschapter, this measurement also provides strong evidence for a cosmologicalconstant.Theonlywayweknowofhavingaflatyetacceleratingcosmos is ifthereisvacuumenergy.

26.BOOMERANG.Thepictureshowsthisexperimentabouttobelaunchedonaballoon inAntarctica.Theexperimentalpayload isperchedon thevehicle totheright.TheflightpathofthisballoontookitaroundtheSouthPole,makinguseofcirculatingwindstoreturnitnearthepointoflaunch.Antarcticaisverydry,makingit thebestplaceonEarthformicrowavebackgroundexperiments,butitisstillbettertogetoutintospaceifpossible.

Thepictureemerging fromstructure studies seems tobe in linewith theotherstrandsIhavediscussed,butwestilldon’tknowhowtheUniversecontrivedtobe the way it is. The answer to this deeper puzzle will rely on deeperunderstandingsofthenatureofmatter,space,andtime.I’lldiscusstheseinthenextchapter.

27. The flatness of space. The top panel here shows the fine-scale pattern oftemperature fluctuations measured by BOOMERANG. Below are simulatedpatternsthattakeintoaccounttheexpectedangularsizeofthesefluctuationsinclosed, flat, and open cosmologies. The best match is with a flat Universe(centre). This strong indication has added impetus to the future experimentsMAPandthePlanckSurveyorthatwillmapthewholeskywiththisresolution.

Chapter8Atheoryofeverything?

Themodern era of physics beganwith two revolutions that took place in theearlyyearsof the twentieth century.Oneof them involved the introductionofrelativity, and it played a major role in the development of cosmologythroughout this century. The other major upheaval was the birth of quantummechanics.Bycontrast,theimplicationsofquantumphysicsforcosmologyarestillfarfromunderstood.

Theworldofthequantum

In the world according to quantum theory, every entity has a dual nature. Inclassical physics two distinct concepts were used to describe distinct naturalphenomena:waves andparticles.Quantumphysics tells us that these conceptsdo not apply separately to the microscopic world. Things that we previouslyimaginedtobeparticlescansometimesbehavelikewaves.Phenomenathatwepreviously thought of as waves can sometimes behave like particles. Lightbehaveslikeawave.Onecanproduceinterferenceanddiffractioneffectsusingprisms and lenses. Moreover, Maxwell had shown that light was actuallydescribed mathematically by an equation called the wave equation: the wavenature of light is therefore predicted by this theory. On the other hand,MaxPlanck’sworkontheradiationemittedbyhotbodieshadalsoshownthatlightcouldalsobehaveasifitcameindiscretepackets,whichhecalledquanta.Hehesitatedtoclaimthat thesequantacouldbeidentifiedwithparticles.ItwasinfactAlbertEinstein,intheworkonthephotoelectriceffectforwhichhewontheNobel Prize, who made the step of saying that light was actually made ofparticles. These particles later became known as photons. But how can

somethingbebothawaveandaparticle?Onehastosaythatrealitycannotbeexactlydescribedbyeitherconcept,butthatitbehavessometimesasifitwereawaveandsometimesasifitwereaparticle.

ImagineamedievalmonkreturningtohismonasteryafterhisfirsttriptoAfrica.Duringhis travelshechancedupona rhinoceros,and is facedwith the taskofdescribing it to his incredulous brothers. Since none of them has ever seenanythingas strangeas a rhino in the flesh,hehas toproceedbyanalogy.Therhinoceros, he says, is in some respects like a dragon and in others like aunicorn.Thebrothersthenhaveareasonablepictureofwhatthebeastlookslike.Butneitherdragonsnorunicornsexistinnature,whiletherhinocerosdoes.Itisthesamewithourquantumworld:realityisdescribedneitherbyidealizedwavesnor by idealized particles, but these concepts can give some impression ofcertainaspectsofthewaythingsreallyare.

Theideathatenergycameindiscretepackets(orquanta)wasalsosuccessfullyappliedtothesimplestofallatoms,thehydrogenatom,byNielsBohrin1913and to other aspects of atomic and nuclear physics. The existence of discreteenergy levels in atoms and molecules is fundamental to the field ofspectroscopy,whichplaysaroleinfieldsasdiverseasastrophysicsandforensicscienceandwascrucialtoHubble’sdiscoveryoftherecessionofthegalaxies.

TheuncertainUniverse

Theacceptanceofthequantizednatureofenergy(andlight)wasonlythestartofthe revolution that founded modern quantum mechanics. It was not until the1920sandtheworkofSchrödingerandHeisenbergthatthedualnatureoflightas both particle and wave was finally elucidated. For while the existence ofphotonshadbecomeaccepted in thepreviousyears, therehadbeennoway toreconcile thiswith thewell-knownwave behaviour of light.What emerged inthe 1920s was a theory of quantum physics built upon wave mechanics. InSchrödinger’s version of quantum theory, the behaviour of all systems isdescribed in terms of a wavefunction (usually called ψ), which evolvesaccording toanequationcalled theSchrödingerequation.Thewavefunctionψdepends on both space and time. Schrödinger’s equation describeswaves thatfluctuateinbothspaceandtime.

So howdoes the particle behaviour come in?The answer is that the quantumwavefunctiondoesnotdescribesomethinglikeanelectromagneticwave,whichonethinksofasaphysical thingexistingatapoint inspaceandfluctuating intime. The quantum wavefunction describes a ‘probability wave’. Quantumtheoryasserts that thewavefunctionisallonecanknowabout thesystem:onecannotpredictwithcertaintyexactlywheretheparticlewillbeatagiventime,justtheprobability.

An important aspect of thiswave-particle duality is theUncertainty Principle.This has many repercussions for physics, but the simplest one involves thepositionofaparticleanditsspeed.Heisenberg’suncertaintyprinciplestatesthatone cannot know the position and speed of a particle independently of oneanother.Thebetteryouknowtheposition, theworseyouknowthespeed,andviceversa.Ifyoucanpinpointtheparticleexactly,thenitsspeediscompletelyunknown. If you know its speed precisely, then the particle could be locatedanywhere. This principle is quantitative, does not apply only to position andmomentum, but also to energy and time and other pairs of quantities that areknownasconjugatevariables.

It is a particularly important consequence of the energy-time UncertaintyPrinciple that empty spacecangivebirth to short-livedparticles that spring inandoutofexistenceonatimescalecontrolledbytheUncertaintyPrinciple.Thisis the reasonwhy particle physicists expect the vacuum to possess energy. Inotherwords,thereshouldbeacosmologicalconstant.Theonlyproblemisthattheydon’tknowhowtocalculateit.Thebestguessesavailablearetoolargebymore than 100 orders of magnitude. But the idea of cosmic uncertainty hasscored one notable success: it is thought to be the reason for the existence ofsmall primordial density fluctuations that started off the growth of cosmicstructure.

A Universe running according to Newtonian physics is deterministic, in thesensethatifoneknewthepositionsandvelocitiesofalltheparticlesinasystemat agiven time thenonecouldpredict theirbehaviour at all subsequent times.Quantummechanicschangedall that,sinceoneof theessentialcomponentsofthistheoryistheprinciplethatatafundamentallevel,thebehaviourofparticlesis inherently unpredictable, hence the need to resort to calculations ofprobability.

Theinterpretationtobeputonthisprobabilisticapproachisopentoconsiderable

debate. For example, consider a system in which particles travel in a beamtowards two closely separated slits.Thewavefunctionψ corresponding to thissituationdisplaysan interferencepatternbecause the ‘probabilitywave’passesthroughboth slits. If thebeam is powerful, itwill consist of hugenumbers ofphotons. Statistically the photons should land on a screen behind the slitsaccordingtotheprobabilitydictatedbythewavefunction.Sincetheslitssetupaninterferencepattern, thescreenwillshowacomplicatedseriesofbrightandfaintbandswhere thewavessometimesaddupinphaseandsometimescanceleach other. This seems reasonable, but suppose we turn the beam down inpower.Thiscanbedoneinsuchawaythatthereisonlyonephotonatanytimetravelling through the slits. The arrival of each photon can be detected on thescreen.Byrunningtheexperimentforareasonablylongtimeonecanbuildupapatternonthescreen.Despitethefactthatonlyonephotonatatimeistravellingthroughtheapparatus,thescreenstillshowsthepatternoffringes.Insomesenseeachphotonmustturnintoawavewhenitleavesthesource,travelthroughbothslits,interferingwithitselfontheway,andthenturnbackintoaphotoninordertolandinadefinitepositiononthescreen.

So what is going on? Clearly each photon lands in a particular place on thescreen.Atthispointweknowitspositionforsure.Whatdoesthewavefunctionforthisparticledoatthispoint?Accordingtooneinterpretation–theso-calledCopenhageninterpretation–thewavefunctioncollapsessothatitisconcentratedat a single point. This happens whenever an experiment is performed and adefinite result is obtained. But before the outcome is settled nature itself isindeterminate:thephotonreallydoesn’tgothrougheitheroneoftheslits:itisina‘mixed’state.Theactofmeasurementchangesthewavefunctionandthereforechanges reality. This has ledmany to speculate about the interaction betweenconsciousness and quantum ‘reality’. Is it consciousness that causes thewavefunctiontocollapse?

A famous illustration of this conundrum is provided by the paradox ofSchrödinger’sCat.Imaginethereisacatinsideasealedroomcontainingavialofpoison.Thevialisattachedtoadevicewhichwillbreakitandpoisonthecatwhenaquantumeventoccurs,forexampletheemissionofanalpha-particlebyalumpofradioactivematerial.Ifthevialbreaks,deathisinstantaneous.Mostofuswouldaccept that thecat is eitheraliveordeadat agiven time.But ifonetakes the Copenhagen interpretation seriously it is somehow both: thewavefunction for the cat comprises a superposition of the two possible states.Only when the room is opened and the state of the cat ‘measured’ does it

‘become’eitheraliveordead.

An alternative to the Copenhagen interpretation is that nothing physicallychanges at all when a measurement is performed. What happens is that theobserver’s state of knowledge changes. If one asserts that thewavefunctionψrepresentswhatisknownbytheobserverratherthanwhatistrueinrealitythenthere is no problem in having it change when a particle is known to be in adefinite state. This view suggests an interpretation of quantum mechanics inwhichatsomelevel thingsmightbedeterministic,butwesimplydonotknowenoughtopredict.

Yet another view is the Many Worlds interpretation. In this, every time anexperimentisperformed(e.g.everytimeaphotonpassesthroughtheslitdevice)theuniverse,asitwere,splitsintotwo:inoneuniversethephotongoesthroughthe left-hand slit and in the other it goes through the right-hand slit. If thishappens for every photon one ends up with an enormous number of paralleluniverses. All possible outcomes of all possible experiments occur in thisensemble.ButbeforeIheadoffintoaparalleluniverse,letmeresumethethreadofthestory.

Themissinglink

I described the standardmodel of fundamental interactions in Chapter 5. Thethreeforcesitincorporatesarealldescribedbyquantumtheories.Thefourthofthe fundamental interactions is gravity. This has proved extremely resistant toefforts tomakeitfit intoaunifiedschemeof things.Thefirststepindoingsowouldinvolveincorporatingquantumphysicsintothetheoryofgravityinordertoproducea theoryofquantumgravity.Despite strenuousefforts, thishasnotyetbeenachieved. If this is everdone, thenext taskwillbe tounifyquantumgravitywithaunifiedtheoryoftheparticleinteractions.

It is ironic that it is general relativity, which really began the modern era oftheoreticalphysics, thatshouldprovide thestumblingblock tofurtherprogresstowardsaunifiedtheoryofalltheforcesofnature.Inmanyways,theforceofgravity isextremelyweak.Mostmaterialbodiesareheld togetherbyelectricalforces between atoms which are many orders of magnitude stronger than thegravitational forces between them. But despite its weakness gravity has a

perplexingnature that seems to resist attempts toput it togetherwithquantumtheory.

28. A theory of everything. The four forces of Nature we know in our low-energy world are thought to become inextricably unified at higher energy.Turning theclockbackon theBigBangwefirstexpect thatelectromagnetismandweakinteractionsmergeintoanelectroweakforce.Athigherenergiesstill,thiselectroweakforcewillunitewiththestrongnuclearforceinaGrandUnifiedTheory(GUT).Athigherenergiesstill,gravitymayjoinintoproduceatheoryofeverything.Itisthistheory,ifitexists,thatwilldescribetheBigBangitself.

Einstein’s general theory of relativity is a classical theory, in the sense thatMaxwell’sequationsofelectromagnetismarealsoclassical;theyinvolveentitiesthataresmoothratherthandiscreteanddescribebehaviourthatisdeterministicrather than probabilistic. On the other hand, quantum physics describes afundamental lumpiness: everything consists of discrete packets or quanta.

Likewise,theequationsofgeneralrelativityallowonetocalculatetheexactstateoftheUniverseatagiventimeinthefutureifsufficientinformationisgivenatsometimeinthepast.Theyarethereforedeterministic.Thequantumworld,onthe other hand, is subject to the uncertainty embodied in Heisenberg’sUncertaintyPrinciple.

Of course, classical electromagnetic theory is perfectly adequate for manypurposes, but the theory does break down in certain situations, such as whenradiationfieldsareverystrong.Forthisreasonphysicistssought(andeventuallyfound) the quantum theory of electromagnetism or quantum electrodynamics(QED). This theory was also made consistent with the special theory ofrelativity,butdoesnotincludegeneral-relativisticeffects.

While Einstein’s equations also seem quite accurate for most purposes, it issimilarly natural to attempt the construction of a quantum theory of gravity.Einstein himself always believed that his theorywas incomplete in this sense,and would eventually need to be replaced by a more complete theory. Byanalogywith the breakdownof classical electromagnetism, one can argue thatthisshouldhappenwhengravitationalfieldsareverystrong,oronlengthscalesthat are extremely short. Attempts to build such a theory have so far beenunsuccessful.

Although there is nothing resembling a complete picture of what a quantumtheoryofgravitymightinvolve,therearesomeinterestingspeculativeideas.Forexample,sincegeneralrelativityisessentiallyatheoryofspace-time,spaceandtime themselves must become quantized in quantum gravity theories. Thissuggests that,althoughspaceandtimeappearcontinuousandsmoothtous,onminuscule scales of thePlanck length (around10–33 cm), space ismuchmorelumpyandcomplicated,perhapsconsistingofa foam-like topologyofbubblesconnectedbytunnelscalledwormholesthatarecontinuallyformingandclosingin the Planck time, which is 10–43 seconds. It also seems to make sense toimaginethatquantizedgravitationalwaves,orgravitons,mightplaytheroleofthegaugebosons inother fundamental interactions, suchas thephotons in thetheoryof quantumelectrodynamics.Asyet, there is no concrete evidence thattheseideasarecorrect.

Thetinyscalesoflengthandtimeinvolvedinquantumgravitydemonstratewhythis quantum gravity is a field for theorists rather than experimentalists. Nodevicehasyetbeenbuiltcapableofforcingparticlesintoaregionoforderthe

Plancklengthor less.Theenormousenergiesrequired todo thisareneededtoreveal the quantum nature of gravity. But that is precisely why so manytheoreticianshave turnedawayfromparticleexperimentsassuch,and towardscosmology.TheBigBangmusthaveinvolvedphenomenaonthePlanckscale,so it may in principle be possible to learn about fundamental physics fromcosmology.

Thebeginningoftime

ThepresenceofasingularityattheverybeginningoftheUniverseisverybadnews for the Big Bang model. Like the black hole singularity, it is a realsingularity where the temperature and density become truly infinite. In thisrespect the Big Bang can be thought of as a kind of time-reverse of thegravitational collapse that forms a black hole. As was the case with theSchwarzschild solution, many physicists thought that the initial cosmologicalsingularity could be a consequence of the special form of the solutions ofEinstein’sequationsusedtomodeltheBigBang,butthisisnowknownnottobe the case. Hawking and Penrose generalized Penrose’s original black holetheoremstoshowthatasingularityinvariablyexistsinthepastofanexpandingUniverse in which certain very general conditions apply. Physical theorycompletely fails us at the instant of the Big Bang where the nasty infinitiesappear.

29.Space-time foam.Oneof the ideasassociatedwithquantumgravity is thatspace-time itself may turn into a seething mass of bubbles and tubes allspringing into existence and disappearing on a timescale comparable to thePlancktime.

Soisitpossibletoavoidthissingularity?Andifso,how?Itismostlikelythatthe initial cosmological singularity might well just be a consequence ofextrapolatingdeductionsbasedontheclassicaltheoryofgeneralrelativityintoasituationwherethis theoryisnolongervalid.This iswhatEinsteinsaysintheparagraph quoted in Chapter 3 during the discussion of black holes.What isneededisquantumgravity,butwedon’thavesuchatheoryand,sincewedon’thave it we don’t know whether it would solve the riddle of the Universe’sapparentlypathologicalbirth.

Thereare,however,waysofavoidingtheinitialsingularityinclassicalgeneralrelativitywithout appealing to quantumeffects. Firstly, one could try to avoidthe singularity by proposing an equation of state for matter in the very earlyUniversethatdoesnotobeytheconditionslaiddownbyHawkingandPenrose.Themostimportantoftheseconditionsisarestrictiononthebehaviourofmatterat highenergies called the strongenergy condition.There arevariousways inwhichthisconditionmightindeedbeviolated.Inparticular,itisviolatedduringthe accelerated expansion predicted in theories of cosmic inflation.Models in

whichthisconditionisviolatedrightattheverybeginningcanhavea‘bounce’rather than a singularity. Running the clock back, the Universe reaches aminimumsizeandthenexpandsagain.

Whether the singularity is avoidable or not remains an openquestion, and theissueofwhetherwecandescribetheveryearliestphasesoftheBigBang,beforethePlanck time,will remainopen at least until a complete theoryof quantumgravityisconstructed.

Time’sarrow

TheexistenceofasingularityatthebeginningoftheUniversecallsintoquestiontheverynature of space, andparticularly of time, at the instant of creation. Itwouldbenicetoincludeatthispointacleardefinitionofwhattimeactuallyis.Everyoneisfamiliarwithwhattimedoes,andhoweventstendtobeorderedinsequences.Weareusedtodescribingeventsthatinvariablyfollowothereventsintermsofachainofcauseandeffect.Butwecan’tgetmuchfurtherthanthesesimple ideas. In the end, the best statement of what is time is that time iswhateveritisthatismeasuredbyclocks.

Einstein’stheoriesofrelativityeffectivelydestroyedtheNewtonianconceptsofabsolutespaceandabsolutetime.Insteadofhavingthreespatialdimensionsandone time dimension which are absolute and unchanging regardless of themotionsofparticlesorexperimenters,relativisticphysicsmergesthesetogetherina single four-dimensionalentitycalledspace-time.Formanypurposes, timeandspacecanbetreatedasmathematicallyequivalentinthesetheories:differentobservers generally measure different time intervals between the same twoevents,butthefour-dimensionalspace-timeintervalisalwaysthesame.

However,thesuccessesofEinstein’stheoreticalbreakthroughstendtomaskthefact that we all know from everyday experience that time and space areessentially different.We can travel north or south, east andwest, but we canonlygoforwardsintimetothefuture,notbackwardsintimetothepast.AndwearequitehappywiththeideathatbothLondonandNewYorkexistatagiventime at different spatial locations. But nobody would say that the year 5001existsinthesamewaythatwethinkthepresentexists.Wearealsohappytosaythatwhatwedonowcausesthingstohappeninthefuture,butdonotconsider

eventsatthesametimeintwolocationsascausingeachother.Spaceandtimereallyarequitedifferent.

On a cosmological level, the Big Bang certainly appears to have a preferreddirection.Buttheequationsdescribingitareagaintime-symmetric.Ouruniversehappens to be expanding rather than contracting, but it could have beencollapsinganddescribedbythesamelaws.Orcoulditbethatthedirectionalityoftimethatweobserveissomehowsingledoutbythelarge-scaleexpansionoftheUniverse?Ithasbeenspeculated,byHawkingandothers,thatifwelivedinaclosedUniversethateventuallystoppedexpandingandbegantocontract,thentimewould effectively run backwards during the contraction phase. In fact, ifthishappenedwewouldnotbeabletotellthedifferencebetweenacontractingUniverse with time running backwards and an expanding Universe with timerunningforwards.Hawkingwasconvincedforatimethatthishadtobethecase,butlaterchangedhismind.

AmoreabstractproblemstemsfromthefactthatEinstein’stheoryisfullyfour-dimensional:theentireworld-lineofaparticle,chartingthewholehistoryofitsmotionsinspace-time,canbecalculatedfromthetheory.Aparticlewhichexistsatdifferent timesexists in the sameway twoparticlesmightexist at the sametimeindifferentplaces.Thisisstronglyatoddswithourideasoffreewill.Doesourfutureexistalready?Arethingsreallypredeterminedinthisway?

These questions are not restricted to relativity theory and cosmology. Manyphysicaltheoriesaresymmetricbetweenpastandfutureinthesamewayastheyare symmetric between different spatial locations. The question of how theperceived asymmetry of time can be reconciled with these theories is a deepphilosophicalpuzzle.Thereareatleasttwootherbranchesofphysicaltheoryinwhichraisethequestionofthearrowoftime,asitissometimescalled.

Oneemergesdirectlyfromaseeminglyomnipotentphysicalprinciple,calledtheSecondLawofThermodynamics.Thisstatesthattheentropyofaclosedsystemneverdecreases.The entropy is ameasureof thedisorderof a system, so thislawmeans that the degree of disorder of a system always tends to increase. Ihaveverifiedthisexperimentallymanytimesthroughperiodicobservationofmyoffice.Thesecondlawisamacroscopicstatement;itdealswithbigthingslikesteamengines,butitarisesfromamicroscopicdescriptionofatomsandenergystates provided by detailed physical theories. The laws governing thesemicrostatesareallentirelyreversiblewithrespecttotime.Sohowcananarrow

oftimeemerge?

Lawssimilartotheclassicallawsofthermodynamicshavealsobeenconstructedto describe the properties of black holes andof gravitational fields in general.Although the definition of the entropy associated with gravitational fields isdifficult to define, these laws seem to indicate that the arrow of time persistseveninacollapsingUniverse.ItwasforthisreasonthatHawkingabandonedhistime-reversalidea.

Another arrow-of-time problem emerges from quantum mechanics, which isagaintime-symmetric,butinwhichweirdphenomenaoccursuchasthecollapseofthewavefunctionwhenanexperimentisperformed.Wavefunctionsappeartodo this only in one direction of time and not the other but, as I have hintedabove, this may well just be a conceptual difficulty arising from theinterpretationofquantummechanicsitself.

Theno-boundaryhypothesis

Spaceandtimeareverydifferentconceptstous,livingaswedoinalow-energyworldfarremovedfromtheBigBang.Butdoesthatmeanthatspaceandtimewerealwaysdifferent?Orinaquantumtheoryofgravitycouldtheyreallybethesame? In classical relativity theory, space-time is a four-dimensionalconstructionwherein the threedimensionsofspaceandonedimensionof timeareweldedtogether.Butspaceandtimearenotequivalent.Oneideaassociatedwith quantum cosmology, developed byHawking togetherwith JimHartle, isthat the characteristic signature of timemay be erasedwhen the gravitationalfield isverystrong.The idea isbasedonan ingenioususeof thepropertiesofimaginarynumbers.(Imaginarynumbersareallmultiplesofthenumberiwhichisdefinedtobethesquarerootofminusone.)ThistinkeringwiththenatureoftimeispartofthenoboundaryhypothesisofquantumcosmologyduetoHartleandHawking.Since,inthistheory,timelosesthecharacteristicsthatseparateitfrom space, the concept of a beginning in time becomesmeaningless. Space-timeswiththissignaturethereforehavenoboundary.ThereisnoBigBang,nosingularity,becausethereisnotime,justanotherdirectionofspace.

ThisviewoftheBigBangisoneinwhichthereisnocreation,becausethewordcreation implies some kind of ‘before and after’. If there is no time then the

Universehasnobeginning.Askingwhathappenedbefore theBigBangis likeaskingwhatisfurthernorththantheNorthPole.Thequestionismeaningless.

I should stress that theno-boundaryconjecture isnotacceptedbyallquantumcosmologists: other ways of understanding the beginning (or lack of it) havebeen proposed. The Russian physicist Alexander Vilenkin proposed analternativetreatmentofquantumcosmologyinwhichthereisadefinitecreation,throughwhichtheuniverseemergesbyaprocessofquantumtunnellingoutofnothing.

Theoriesofeverything

Ihave tried todescribe justa fewof theareas inwhichparticlephysicistsandcosmologists have been attempting to weld together quantum physics andgravitytheory.Thisisonestepinthedirectionofwhatmanyphysicistsfeel istheultimategoalofscience:towritethemathematicallawsdescribingallknownforcesofnatureintheformofoneequationthatyoumight,perhapsifyouhavenodress-sense,wearonyourT-shirt.

Thelawsofphysics,sometimesalsocalledthelawsofnature,arethebasictoolsof physical science. They comprise mathematical equations that govern thebehaviourofmatter(in theformofelementaryparticles)andenergyaccordingto the various fundamental interactions described above. Sometimesexperimental results obtained in the laboratory or observations of naturalphysical processes are used to infer mathematical rules which describe thesedata.Othertimesatheoryiscreatedfirstastheresultofahypothesisorphysicalprinciplewhichreceivesexperimentalconfirmationonlyatalaterstage.Asourunderstanding evolves, seemingly disparate physical laws become unified in asingleoverarchingtheory.Theexamplesgivenaboveshowhowinfluentialthisthemehasbeenoverthepasthundredyearsorso.

But there are deep philosophical questions lying below the surface of all thisactivity. For example, what if the laws of physics were different in the earlyUniverse?Couldonestillcarryoutthiswork?Theanswertothisisthatmodernphysical theories actually predict that the laws of physics do change. As onegoestoearlierandearlierstagesintheBigBang,forexample,thenatureoftheelectromagnetic and weak interactions changes so that they become

indistinguishableatsufficientlyhighenergies.Butthischangeinthelawisitselfdescribed by another law: the so-called electroweak theory. Perhaps this lawitselfismodifiedatscaleswheregrandunifiedtheoriestakeprecedence,andsoonrightbacktotheverybeginningoftheUniverse.

Whatever the fundamental rules are, however, physicists have to assume thatthey apply for all times since the Big Bang. It is merely the low-energyoutcomes of these fundamental rules that change with time. Making thisassumption,theyareabletobuildacoherentpictureofthethermalhistoryoftheUniversewhichdoesnotseemtobeinmajorconflictwiththeobservations.Thismakesthisassumptionreasonable,butdoesnotproveittobecorrect.

Another setof importantquestions revolvesaround the roleofmathematics inphysicaltheory.Isnaturereallymathematical?Oraretheruleswedevisemerelyakindof shorthand to enable us to describe theUniverse on as fewpieces ofpaper as possible?Dowe discover laws of physics or dowe invent them? Isphysicssimplyamap,orisittheterritoryitself?

Thereisalsoanotherdeepissueconnectedwiththelawsofphysicspertainingtotheverybeginningofspaceandtime.Insomeversionsofquantumcosmology,forexample,onehastoposittheexistenceofphysicallawsthatexist,asitwere,in advance of the physical universe they are supposed to describe. This hascaused many theoreticians to adopt a philosophical approach that mirrors theideasofPlato. In thePlatonic tradition, trueexistencebelongs to the idealizedworldofformratherthanourimperfectworldofthesenses.TotheNeoplatoniccosmologists, what really exists are the mathematical equations of the (yetunknown) theory of everything, rather than the physical world of matter andenergy.Ontheotherhand,notallcosmologistsgetcarriedawayinthismanner.TothoseofamorepragmaticdispositionthelawsofphysicsaresimplyaneatdescriptionofourUniversewhosesignificanceliessimplyintheirusefulness.

There have been many attempts to produce theories of everything, involvingsuchexoticideasassupersymmetryandstringtheory(orevenacombinationofthe two known as superstring theory). In superstring theory, particles are nottreated as particles at all but as oscillations in one-dimensional entities calledstrings. The different modes of vibration string loops correspond to differentparticles.Thestringsthemselvesliveinaspaceoftenortwenty-sixdimensions.Ourspace-timehasonlyfourdimensions(threespaceandonetime),sotheextradimensions must be hidden. Perhaps they are wrapped up so small that they

cannotbeobserved.Aftermuchexcitement in the1980s this ideawentoutoffashion, largely due to the technical complexity involved in handling suchcomplicated multidimensional objects. More recently, these ideas haveexperienced a kind of renaissance, with the generalization of the concept ofstrings into ‘branes’, higher-dimensional objects whose name derives from‘membrane’, and the realization that there is, in effect, a single theory (called‘M-theory’)describingallversionsofthiskindofapproach.Theseareexcitingideas but they are relatively undeveloped; string theory has not yetmade anyclear predictions that have impacted on cosmology. It remains to be seenwhetherthegrander-than-grandunificationtowhichtheseapproachesaspirecanactuallyberealized.

The search for a theory of everything also raises interesting philosophicalquestions. Some physicists, Hawking among them, would regard theconstructionofatheoryofeverythingasbeing,insomesense,readingthemindofGod,oratleastunravellingtheinnersecretsofphysicalreality.Otherssimplyarguethataphysicaltheoryisjustadescriptionofreality,ratherlikeamap.Atheorymightbegoodformakingpredictionsandunderstandingtheoutcomesofobservationorexperimentbutit isnomorethanthat.Atthemomentweuseadifferentmapforgravityfromtheoneweuseforelectromagnetismorforweaknuclearinteractions.Thismaybecumbersome,butitisnotdisastrous.Atheoryofeverythingwouldsimplybeasinglemap,ratherthanasetofdifferentonesthatoneusesindifferentcircumstances.Thislatterphilosophyispragmatic.Weusetheoriesforthesamereasonsthatweusemaps:becausetheyareuseful.ThefamousLondonUndergroundmapiscertainlyuseful,butitisnotaparticularlyaccuraterepresentationofphysicalreality.Nordoesitneedtobe.

Andinanycaseonehastoworryaboutthenatureofexplanationaffordedbyatheory of everything. How will it explain, for example, why the theory ofeverything is what it is and not some other theory? To my mind, this is thebiggest problem of all. Can any theory based on quantum mechanics becomplete in any sense, when quantum theory is in its nature indeterministic?Moreover,developmentsinmathematicallogichavecastdoubtontheabilityofanytheorytobecompletelyself-contained.ThelogicianKurtGödelhasproveda theorem, known as the incompleteness theorem, that shows that anymathematical theorywillalwayscontain things thatcan’tbeprovedwithin thetheory.

TheAnthropicPrinciples

Cosmologyhas alwaysbeen aboutMan’s attempts to understand theUniverseandhis relationship to it.Asscientificcosmologyhasevolved,Man’s rolehasdiminished. Our existence appears accidental, unplanned, and incidental towhatever purpose the cosmoswas constructed to fulfil.This interpretationhasmore recently been challengedby a suggestion called theAnthropicPrinciple,thattheremight,afterall,beadeepconnectionbetweentheexistenceoflifeandthefundamentalphysicsthatgovernshowtheUniverseevolves.ItwasBrandonCarter who first suggested adding the word ‘Anthropic’ to the usual‘CosmologicalPrinciple’tostressthefactthatourUniverseis‘special’,atleasttotheextentthatithaspermittedintelligentlifetoevolvewithinit.

There aremanyotherwiseviable cosmologicalmodels that are not compatiblewith the observation that human observers exist. For example, we know thatheavy elements like carbon and oxygen are vital to the complex chemistryrequiredforterrestriallifetohavedeveloped.Wealsoknowthatittakesaround10 billion years of stellar evolution for generations of stars to synthesizesignificantquantitiesoftheseelementsfromtheprimordialgasofhydrogenandheliumthatexistsintheearlystagesofaBigBangmodel.Weknowthereforethat we could not inhabit a universe younger than about 10 billion years old.SincethesizeoftheUniverseisrelatedtoitsageifitisexpanding,thislineofreasoningshedssomelightonthequestionofwhytheUniverseisasbigasitis.Ithastobebig,becauseithastobeoldiftherehasbeentimeforustoevolvewithin it. This form of reasoning is usually called the ‘Weak’ AnthropicPrincipleanditcanleadtousefulinsightsintothepropertiesourUniversemightbeexpectedtopossesssimplybyvirtueofourpresencewithinit.

Some cosmologists have sought to extend theAnthropic Principle into deeperwaters.While theweak version applies to physical properties of ourUniversesuchas its age, density, or temperature, the ‘Strong’AnthropicPrinciple is anargumentaboutthelawsofphysicsaccordingtowhichthesepropertiesevolve.Itappears that thesefundamental lawsareveryfinelytunedtopermitcomplexchemistry, which, in turn, permits the development of biology and ultimatelyhuman life. If the laws of electromagnetism and nuclear physics were onlyslightlydifferent,chemistryandbiologywouldbeimpossible.Onthefaceofit,thefactthatthelawsofnaturedoappeartobetunedinthiswayseemstobeacoincidence,inthatthereisnothinginourpresentunderstandingoffundamental

physics that requires the laws to be conducive to life in this way. This isthereforesomethingweshouldseektoexplain.

Insomeversionsof thestrongAnthropicPrinciple, thereasoningisessentiallyanargumentfromdesign:thelawsofphysicsareastheyarebecausetheymustbelikethatforlifetodevelop.Thisistantamounttorequiringthattheexistenceof life is itself a law of nature, and the more familiar laws of physics aresubordinatetoit.Thiskindofreasoningappealstosomewithareligiousframeofmindbutitsstatusamongscientistsisrightlycontroversial,asitsuggeststhattheUniversewasdesignedspecificallyinordertoaccommodatehumanlife.

Analternative,andperhapsmorescientific,constructionofthestrongAnthropicPrinciple involves the idea that our Universe may consist of an ensemble ofmini-universes,eachonehavingdifferentlawsofphysicstotheothers.Thismaybewhatemerges fromaunified theory, inwhich thehigh-energysymmetry isbrokeninadifferentwayindifferentpatchesoftheUniverse.Obviously,wecanonlyhaveevolvedinoneofthemini-universescompatiblewiththedevelopmentof organic chemistry and biology, sowe should not be surprised to be in onewhere the underlying laws of physics appear to have special properties. Thisprovidessomekindofexplanationfortheapparentlysurprisingpropertiesofthelawsofnaturementionedabove.Thisisnotanargumentfromdesign,sincethelawsofphysicscouldvaryhaphazardlyfrommini-universetomini-universe.

This version of theAnthropic Principle is rightly controversial, but it at leastaddressesthedistinctionbetweenthe‘how’andthe‘why’.Itremainstobeseenwhether cosmology can explainwhy the Universe is the way it is, but we’vecertainlycomealongwaytowardsunderstandingwhathappened,andhow.

Epilogue

Cosmology is inmanyways similar to forensic science.Neither cosmologistsnor forensic scientists canperformexperiments that recreatepast eventsunderslightly different conditions, which is what most other scientists do. There isonlyoneUniverse,onesceneofthecrime.Inbothfieldstheavailableevidenceis often circumstantial, difficult to gather, and open to ambiguity ofinterpretation.Despitethesedifficulties,thecaseinfavouroftheBigBangis,inmyview,provenbeyondallreasonabledoubt.

Of course, important questions remain unresolved. We still do not know theformofmostofthematterintheUniverse.WedonotknowforsurewhethertheUniverse is finite or infinite. We do not know how the Universe began, orwhether inflation happened. Nevertheless, the points of agreement betweentheoryandobservationaresomanyandsostrikingthatthepiecesofacoherentpicture seemat last to be falling intoplace.But, as the sayinggoes, these arefamouslastwords.

Furtherreading

GeneralreferencesColes,P.(ed.),TheRoutledgeCompaniontotheNewCosmology(London:Taylor&Francis,2001).

Gribbin,J.,CompaniontotheCosmos(London:OrionBooks,1997).Ridpath, I. (ed.), The Oxford Dictionary of Astronomy (Oxford: OxfordUniversityPress,1997).

Chapter1Barrow, J. D., The World Within the World (Oxford: Oxford UniversityPress,1988).

Harrison, E.,Darkness at Night (Cambridge, Mass.: Harvard UniversityPress,1987).

Hoskin, M. (ed.), The Cambridge Illustrated History of Astronomy(Cambridge:CambridgeUniversityPress,1997).

Lightman, A., Ancient Light: Our Changing View of the Universe(Cambridge,Mass.:HarvardUniversityPress,1991).

North, J., The Fontana History of Astronomy and Cosmology (London:Fontana,1994).

Chapter2Coles,P.,Einsteinand theBirthofBigScience (Cambridge: IconBooks,2000).

Pais,A.,‘SubtleistheLord…’:TheScienceandtheLifeofAlbertEinstein(Oxford:OxfordUniversityPress,1992).

Thorne,K. S.,BlackHoles and TimeWarps (NewYork:Norton&Co.,1994).

Chapter3Eddington, A. S., The Nature of the Physical World (Cambridge:CambridgeUniversityPress,1928).

Trope,E.A.,Frenkel,V.Y.,andChernin,A.D.,AlexanderA.Friedmann:The Man who Made the Universe Expand (Cambridge: CambridgeUniversityPress,1993).

Chapter4Florence,R.,ThePerfectMachine:BuildingthePalomarTelescope(NewYork:HarperCollins,1994).

Graham-Smith,F., andLovell,B.,Pathways to theUniverse (Cambridge:CambridgeUniversityPress,1988).

Hubble,E.,TheRealmof theNebulae (Newhaven:YaleUniversityPress,1936).

Preston, R.,First Light: The Search for the Edge of the Universe (NewYork:RandomHouse,1996).

Chapter5Barrow, J.D., andSilk, J.,TheLeftHandofCreation (NewYork:BasicBooks,1983).

Close,F.,TheCosmicOnion(London:Heinemann,1983).Davis,P.C.W.,TheForcesofNature(Cambridge:CambridgeUniversityPress,1979).

Pagels,H.R.,PerfectSymmetry(Harmondsworth:PenguinBooks,1992).Silk,J.,TheBigBang,rev.andupdatededn.(NewYork:W.H.Freeman&Co.,1989).

Weinberg,S.,TheFirstThreeMinutes(London:Fontana,1983).

Chapter6Gribbin, J., and Rees,M. J.,The Stuff of the Universe (Harmondsworth:PenguinBooks,1995).

Guth,A.H.,TheInflationaryUniverse(NewYork:JonathanCape,1996).Krauss,L.M.,TheFifthEssence(NewYork:BasicBooks,1989).Livio, M., The Accelerating Universe (New York: John Wiley & Sons,2000).

Overbye,D.,TheLonelyHeartsoftheCosmos(NewYork:HarperCollins,

1991).Rees,M.J.,JustSixNumbers(London:Weidenfeld&Nicolson,1999).Riordan,M.,andSchramm,D.,TheShadowsofCreation(Oxford:OxfordUniversityPress,1993).

Chapter7Chown,M.,TheAfterglowofCreation(London:ArrowBooks,1993).Cornell,J.(ed.),Bubbles,VoidsandBumpsinTime:TheNewCosmology(Cambridge:CambridgeUniversityPress,1989).

Smoot,G.,andDavidson,K.,Wrinkles inTime (NewYork:AvonBooks,1993).

Chapter8Barrow, J. D., Theories of Everything (Oxford: Oxford University Press,1991).

——PiintheSky(Oxford:OxfordUniversityPress,1992).——TheOriginoftheUniverse(London:OrionBooks,1995).Coles,P.,HawkingandtheMindofGod(Cambridge:IconBooks,2000).Hawking, S. W., A Brief History of Time (New York: Bantam Books,1988).

Lidsey, J.E.,TheBiggerBang (Cambridge:CambridgeUniversityPress,2000).

Index

A

Abellclusters95–6acceleratinguniverse11,56,91–2ageoftheUniverse54–6Almagest5Alpher,R.62Anaximander4AndromedaNebula47,94–5anthropicprinciple125–7antimatter68,72–3Aquinas,T.5Aristotle5,7arrowoftime117–20

B

Babylon2–3baryons64,68,72–3,80baryoncatastrophe83baryonnumber72Bethe,H.62BigBang8–11,37–8,57–73,115–17blackbody59–61

blackholes24–6,115–16,120Bondi,H.58BOOMERANG105–6bosons67–70Brahe,T.6,89branes123

C

C-field58carbon125carbondating54Cepheidvariables51–3CERN65Chandrasekharmass90China2–3classicalphysics114closedUniverse10,34,78,118clustersofgalaxies81,95–6COBE(CosmicBackgroundExlorer)98–100,102continuouscreation58Comacluster17–18,96Copenhageninterpretation111–12CopernicanPrinciple29–30,43–4,81Copernicus,N.5,7cosmicmicrowavebackground8–9,30,59–61,73cosmologicalconstant31,91–2cosmologicalflatnessproblem,seeflatnessproblemCosmologicalPrinciple29–30,32–3,43–4,75,98PerfectCosmologicalPrinciple58–9cosmography93–106curvedspace20–26,77–8

D

darkmatter11,71,81–5colddarkmatter101–2deSitter,W.8,46deceleratinguniverse54–6,77determinism111–12,114,124deuterium62–3deuteriumbottleneck64DickeR.59dipoleanisotropy98Dirac,P.A.M.67distanceindicators51–3Dopplereffect41–2,98Dopplershift,seeDopplereffect

E

Eddington,A.S.43Einstein,A.7,11,14–26,28–38‘biggestblunder’30–1electromagnetism12,15,67,70,113–14electrons61,68–9electroweaktheory70–1,113,122energy75–6entropy119EnumaElish2equivalenceprinciple,seeprincipleofequivalenceescapevelocity76Euclid’sgeometry10,21–2,35expandingUniverse8,39–53

F

fermions67–70Feynman,R.67

filaments96flatUniverse10–11,33,78flatnessproblem86–7fractal96Friedmann,A.8Friedmannmodels32–4,45–6,75–8,86,99

G

galaxies7–8,26,40,47,51–2,58galaxyclusters,seeclustersofgalaxiesGalileo15Gamow,G.62gaugebosons,seebosonsgedankenexperiments15–19generalrelativity,seegeneraltheoryofrelativitygeneraltheoryofrelativity7–8,20–6,28–9,74–5Glashow,S.L.70globularclusters56,79gluons70Gödel,K.124Gold,T.58gravitons115gravity12–14,67,112gravitationalinstability99gravitationallensing84gravitationalwaves115grandunifiedtheory(GUT)71GreatWall96Greekcosmology4–5GUT,seegrandunifiedtheoryGuth,A.87

H

Ho,seeHubble’sconstanthadrons68Hartle,J.M.120Hawking,S.37,116–18,120HeatDeathoftheUniverse6Heisenberg,W.108seealsouncertaintyprinciplehelium62–4,125Herman,R.62Hipparchos51Higgs71homogeneity29,45,58seealso,CosmologicalPrincipleHoyle,F.57–8Hubble,E.7–8,43Hubble’sconstant48–56,75,78Hubble’slaw39–47HubbleDeepField10HubbleSpaceTelescope(HST)10,53,101–2hydrogen62,125

I

incompletenesstheorem124inflation11,30,73,87–8isotropy29–30,45,58,61seealsoCosmologicalPrinciple

K

Kepler,J.6,7Kepler’sstar89

L

Laplace25LargeMagellanicCloud90Lemaître,G.8,32,43–4leptons67–8LocalGroup95large-scalestructure93–106leptons67–9LickMap93,95lifeintheUniverse125–7lithium62

M

Mtheory123Mach’sPrinciple29ManyWorldsinterpretation112MAP(MicrowaveAnisotropyProbe)10,84,104Marduk2–3MAXIMA105Maxwell,J.C.15Maxwell’stheory15,64,70Michell,J.25MilkyWay7–8,30,50,52,89mythology1–4

N

Narlikar,J.V.N.58nebulae,seegalaxiesneutrinos67–8neutrons62–4Newton,I.6

Newtonianmechanics13,27–8,110no-boundaryhypothesis120–1nucleosynthesis62–4,80

O

Olbers’Paradox7Omega(Ω)74–92openUniverse10,34,56,78oxygen125

P

PanGu2–3parallax50–1paralleluniverses,seeManyWorldsinterpretationPeebles,P.J.E.59Penrose,R.37,116–17Penzias,A.8,59phasetransitions11photons67–70,108–11Planck,M.107Plancktime115;117Plancklength115PlanckSurveyor10,84,104Plato4–5Platonismincosmology6,123Principia6principleofequivalence17–19principleofrelativity7–8protons62–4Ptolemy5

Q

QCD69–70QED67–70,114quantumchromodynamics,seeQCDquantumelectrodynamics,seeQEDquantumphysics107–14quantumgravity66,88,112–14,117quarks68–70,88quasars66

R

radioactivity54–5recombination61redshift42–7,90,94–5,102relativity,generaltheoryof,seegeneraltheoryofrelativityrelativity,principleof,seeprincipleofrelativityrelativity,specialtheoryof,seespecialtheoryofrelativityripples10,98–100,102–4Ryle,M.58

S

Sakharov,A.72–3Salaam,A.70Sandage,A.R.79Schrödinger,E.108Schrödingerequation109Schrödinger’scat111Schwarzschild,K.25–6Schwarzschildradius26Schwarzschildsolution26,36,115Shapleyconcentration96

singularity9,34,36–7,115–17naked37Slipher,V.40space,curved,seecurvedspacespace-time8,10,32,117–20‘foam’115–16specialrelativity,seespecialtheoryofrelativityspecialtheoryofrelativity14–17spectroscopy40–3staticuniverse30–1standardmodelofparticlephysics71SteadyState57–9stringtheory57stronganthropicprinciple125strongenergycondition117strongnuclearforce12,70,113superclusters97–8supernovae51,89–91superstrings123symmetry28–9,70,117supersymmetry71,123

T

Thales4thermodynamics6secondlaw119theoriesofeverything121–5Tiamat2–3time117–18two-degreefieldsurvey94,97

U

uncertaintyprinciple108–14

V

vacuumenergy92,106seealsocosmologicalconstantVilenkin,A.121Virgocluster53,96voids96–8

W

wavefunction108–11weakanthtropicprinciple,seeanthropicprincipleweaknuclearforce12,69–70,113Weinberg,S.70Wilson,R.8,59

X

X-rays83