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The Observable Universe

Space is big. Really big. You just wont believe how vastly hugely mind-bogglingly big it is. I mean, you may think its a long way down the road to thechemist, but thats peanuts to space. Douglas Adams, The Hitchhikers Guide

to the Galaxy.

This chapter opens the story as we discuss the observed Universe and note the apparentproblems we find in trying to describe that universe. We will see that the standard BigBang picture is very useful for explaining the observable Universe, but is not quite enoughto solve the problems where the Universe came from and how it evolved. It appears thatthe Universe could not have arisen from generic initial conditions, but seems to have evolvedfrom a very finely-tuned origin.

1 What Do We See?

Looking out at the night sky, one cant help but be awed by the vast scales open before them.Even the naked eye can detect hundreds or thousands of stars (depending on whether yourelooking from the city or middle of nowhere). The eye of the Hubble space telescope hasdetected countless more. Figure 1 shows the Ultra Deep Field [1]. This image was formedover a period of several months by focusing the Hubble telescope on a patch of sky roughlyone-tenth of the size of the full moon. This patch was previously thought to be empty, whenviewed from other telescopes. Almost every point of light in the image is a galaxy, containingroughly a hundred billion stars! This image shows the Universe as it was roughly 13 billionyears ago, which is only a few hundred million years after the Big Bang. It is already easyto see that the Universe is big!

It is the goal of physics in general (and cosmology, specifically) to try to explain wherethe Universe came from and how it evolves. As we will see, this will not be an easy task, ingeneral. The attempt to describe the Universe will lead us into new and exciting areas ofphysics, including Einsteins General Theory of Relativity, as well as the laws of quantummechanics. The work done in achieving the goal will be well-worth it, however.

To begin our journey, lets start by making some observations about the Universe. Wewill find that these observations lead to some very interesting puzzles which will require somenew ideas to address. It will, in fact, be our goal to solve these puzzles. We will discuss theseobservations and puzzles in quantitative detail later, and so we now focus on a qualitativediscussion.

1.0.1 The Universe is Very Old and Very Big.

Weve already seen that the Universe is extremely large. The visible Universe extends outto some 1026 meters. However, there are many reasons to expect that the actual Universe ismuch larger! Clearly for these sorts of distances the meter is a very bad unit of measure touse. Just as when we use nanometers to discuss quantum-level phenomenon, we should liketo find a more convenient unit of measure for very large distances.

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Figure 1: The Hubble Ultra Deep Field, shows an estimated 10,000 galaxies. Nearly everypoint of light in the image is a galaxy!

One useful method of measuring distance would be to use the distance that light travelsin some amount of time, typically taken to be one year. This distance, which is about

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meters, is called a light-year, and measures distance and not time! This is a verylarge distance; Pluto orbits the Sun at an average distance on order of about 105 lightyears. Proxima Centauri, the nearest star (other than the Sun), is about 4.22 light yearsaway. The observable Universe extends out to about 5 1010 light years.

The light year is still not the conventional unit of measurement, however. The unit thathas been adopted is the megaparsec, Mpc, or one million parsecs. A parsec is defined as thedistance away such that the Earth-Sun separation distance (about 150 million kilometers)subtends an angle of one second of arc, and corresponds to a distance of about 3.1 1016

meters, or about 3.26 light years. So, a megaparsec is about 3.26 million light years, andcorresponds roughly to the distance between galaxies. The observable Universe is of order14,000 Mpc.

We might expect that such a large system has been around for a long time, one mighteven expect infinitely long. Even based only on the observations from carbon-dating rockshere on Earth, we know that the Universe must be billions of years old. This measurementis also corroborated by our observations of the amounts of hydrogen and helium in the Sun,and knowledge of the fusion reaction rates, and so on. We will get a better estimate in ourdiscussion below where we actually find a finite lifetime for the Universe!

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1.0.2 The Universe Looks Pretty Much the Same Everywhere.

If we look out at the sky in our own solar system we see a nice variety of things: the Sun,some nearby planets, the asteroid belt, etc. The solar system certainly doesnt look the samefrom place to place as we move around. Suppose we pull back far from our solar system, andplace ourselves midway between the Sun and Proxima Centauri. Then, if we look around,the view is a little bit more similar in each direction. Although we do have some differenceshere and there. If we look up, out of the plane of our own galaxy, then we might see theAndromeda Galaxy in one direction, and not in the other. So, it seems like the Universedoes not look the same in every direction.

Suppose we instead go out to very large scales, on the order of megaparsecs. In thiscase we are looking at the sky in terms of galaxies, instead of stars, and our view in everydirection would be very much like that in Figure 1. At such scales, we become blind to thesmall details that differentiate one place or direction from another. On very large scales, theUniverse is homogeneous and isotropic.

Homogeneity and isotropy are not the same things. Homogeneity means that the Universe

is the same from one place to another (meaning that there is no preferred place), whileisotropy means that it is the same in every direction (meaning that there is no preferreddirection). A system can be everywhere homogeneous, but not isotropic. Consider, forexample, a uniform electric field pointing everywhere along the x direction. This system iseverywhere homogeneous, since we can move from place to place and still see the same field,but it is not isotropic since the field points along a specific direction. The electric field of apoint charge is isotropic about that charge, but it is not homogeneous, since the field looksvery different if we move anywhere at all. However, a system that is isotropic about everypoint is necessarily homogeneous, as well. The Universe on the biggest observable scaleslooks both homogeneous and isotropic.

We dont need to rely only on our intuition about the Universe on large scales, or evenimages like that in Figure 1, to imagine the homogeneity and isotropy of the Universe. Figure2 shows the galaxy map, covering more than 930,000 galaxies, obtained by the Sloan DigitalSky Survey [2] over a period of eight years, covering a quarter of the sky, with the Earthat the center. Each point is a galaxy, comprised of about 100 billion stars, and the colordenotes the age of the stars in the galaxy with redder points showing galaxies comprisedof mostly older stars. The units of redshift will be discussed later, but may be taken tobe an indication of distance. Figure 2 ranges over a distance of a little more than half amegaparsec, which is about 2 billion light years. Even on these small scales we can beginto see some of the homogeneity and isotropy of the Universe. We can also begin to see theweb-like structure of the galaxies, forming galactic filaments which are the largest known

structures in the Universe.We can see the homogeneity and isotropy of the Universe in a much more dramaticway. Looking out into the sky, in every direction, we see a faint microwave glow, originallydiscovered back in 1964. This glow, called the Cosmic Microwave Background (CMB), hasbeen measured very precisely by the Wilkinson Microwave Anisotropy Probe (WMAP) [3],and is seen in the whole sky map in figure 3. The CMB has a spectrum as though itwas emitted by a blackbody, with an average temperature of about 2.725 Kelvins to anextraordinary accuracy. The temperature fluctuations, T/T, are of the order O (105)!

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Figure 2: The SDSS Galaxy Map. The map has a range of about 2 billion light years, withthe Earth at the center. Each point on the map is a galaxy, with redder points correspondingto older galaxies.

As well discuss in detail later, the redder regions are slightly warmer, corresponding to

regions which are slightly underdense, while the more blue regions are cooler, correspondingto regions that are slightly overdense (these density fluctuations are also of the same order asthe temperature fluctuations; if the background density is , then / O (105)). As wewill see later, the CMB is a snapshot of the early Universe, and provides the most strikingevidence of the homogeneity and isotropy that we have found.

While we have seen that the Universe is homogeneous and isotropic on the largest ob-servable scales, we must not forget that it seems very inhomogeneous on the smallest scales;the environment in the neighborhood of a star looks very different from that in interstel-lar space. To ignore the tiny deviations from homogeneity would be to ignore stars, andeven individual galaxies. Any theory of the Universe must, therefore, not only explain thelarge-scale properties of the Universe, but also the tiny variations. Furthermore, as we will

discuss later, there is reason to believe that our observable Universe may be only an islandUniverse in a larger structure often called the Multiverse, which is again inhomogeneous.We will discuss these ideas in more detail later.

1.0.3 Parallel Lines Never Seem to Intersect.

Its a well-known fact that the shortest distance between two points is a straight line, andthat two parallel lines never intersect. This is only true on a plane. If we were to draw to

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Figure 3: The Cosmic Microwave Background pervades the entire Universe and has a black-body spectrum with a temperature of about 2.725 Kelvins, with fluctuations of only about105.

parallel lines on a ball, or on the surface of a saddle, then things may not be so simple. Youmay know that airplanes do not travel along straight line paths, but rather curved paths.This is because (as well discuss in detail later) the shortest distance between two points ona sphere (the Earth), is a curved path, a section of a great circle. Because the surface overwhich the line is being drawn is curved, the line itself will be curved.

This can lead to some very interesting behavior. For example, on a sphere two parallellines can intersect (think about lines of longitude meeting at the north pole). Also, the sum

of the angles of a triangle can be different than 180; on a sphere the angles are greater than180 (again - think of the triangle formed by the equator and two lines of longitude), whileon a saddle the angles can be less (the verticies get pinched together). This observationallows for a method of determining whether a surface is curved without actually looking atit from the outside: draw a triangle and see if the angles add up to 180. However, onehas to be careful. If the size of the sphere was large enough, then any measurements (i.e.,adding the angles of triangles) would have negligible errors and the space would look flat.This is because if we get in close enough to a curved surface, it eventually looks flat, like thesurface of the Earth. In order to see any deviations from flatness we would need to draw abig triangle, whose sides are of the order of the radius of the sphere.

While its often taken for granted that the space that we live in is flat, this does notnecessarily have to be the case. We could be living in a curved space, like a sphere. Becausespace is so large we would need to look at the biggest things in the Universe, which is thewhole-sky CMB map seen in figure 3. The temperature fluctuation spots on the CMB havea certain angular separation on the sky, which provides our triangle for measuring flatness.If the intervening space is curved, then the light would also travel along curves, and theapparent size of the spots would be different. Theoretical calculations can predict the sizeof these spots. If the space is flat then the spots would have the angular size predicted by

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theoretical calculations. If the geometry of space was like a sphere, then the light comingfrom the spots would span a larger angle and so would appear larger. If the geometry ofspace was like a saddle, then the light coming from the spots would span a smaller angle,and so would appear smaller.

To a very good degree, it is found that the Universe is approximately flat. This will turn

out to have very important consequences for the evolution, and ultimately the fate, of theUniverse. As we will see, a Universe of zero or negative curvature (like a plane or a saddle,respectively) will exist indefinitely into the future, while one of positive curvature (like asphere) will not! Again, we will return to these issues later.

1.0.4 The Universe is Filled with Good Things.

Just a glance at figure 1 tells us that the Universe is not empty. It is filled with stars, clusteredtogether into galaxies. The stars are mostly hydrogen and helium (and trace amounts ofheavier elements), and therefore are made out of atoms. The atoms are composed of protonsand neutrons in the nucleus, circled by electrons in orbit around them.

The electrons are elementary particles (as far as we can tell), but the protons and neutronshave been found to be composite particles, constructed of quarks which are elementary.There are six different flavors of quark, listed in Table 1.

Quarks

Particle Mass (GeV/c2) Charge (qp)

Up (u) 0.003 2/3Down (d) 0.006 -1/3Charm (c) 1.3 2/3Strange (s) 0.1 -1/3

Top (t) 175 2/3Bottom (b) 4.3 -1/3

Table 1: The Six Flavors of Quarks.

Also given in the table is the mass of each quark, in units of GeV/c2 (as is common inparticle physics), as well as its electric charge, expressed in terms of the proton charge, qp.The proton is composed of two up quarks and one down quark, giving a net charge of +1.The neutron is composed of two down quarks and one up quark for a net charge of zero.

The quarks comprise one class of particles which interact through the strong force, which

well discuss soon. This class of strongly-interacting particles are called hadrons (hadronsactually refer to the strongly-interacting quark composites, baryons and mesons). There isanother class of elementary particles which do not interact via the strong force. This classis called leptons, the most familiar of which is the electron. The various leptons are listedin Table 2, including again the mass and charge. Each of the three charged leptons has anassociated neutrino.

Each of the particles listed in Tables 1 and 2 is a spin 1/2 fermion, and interacts via atleast two forces. Lets take a moment to recall the different forces.

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Leptons

Particle Mass (GeV/c2) Charge (qp)

Electron (e) 0.000511 -1Muon () 0.106 -1

Tau () 1.7771 -1

Electron neutrino (e) < 108 0Muon neutrino () < 0.0002 0

Tau neutrino () < 0.02 0

Table 2: The Six Leptons.

There is, of course, electromagnetism, which gives an interaction between electricalcharges. It was discovered long ago that electricity and magnetism are not two different phe-nomena, but are really different aspects of the same electromagnetic field. It was Maxwells

grand discovery in the 19th century that blended together not only electricity, and mag-netism, but also light into one elegant theory. Electromagnetism is responsible for holdingtogether atoms and molecules, and therefore everyday objects such as tables and people.

The positively-charged protons would tend to blow apart the nucleus if there was notsome additional non-electrical force holding it together. This new force is called the strongforce, and operates on both protons and neutrons, holding the nucleus together. However,if the nucleus gets too big, then the strong force doesnt quite hold it together - some piecesmight fly off, as in alpha-decay. In alpha decay an particle (a helium nucleus) breaks offof a larger nucleus (say uranium). This means that the strong force is not long-range, buthas a finite range, typically operating on nuclear scales, 1015 meters.

There are other types of nuclear decay, for example beta decay, where beta particles

(electrons) are emitted. One example of a system undergoing beta decay is a free neutron.Outside the nucleus a neutron is not stable, but decays after about 15 minutes, or so. Itdecays into a proton, an electron and the antimatter partner to the electron-type neutrino(well discuss antimatter soon). Because the protons and neutrinos are not elementary, itis really the quarks interacting through the force, with a down quark decaying into an upquark, plus an electron and antineutrino. This interaction has to be mediated by someforce, but the leptons do not experience the strong force, and neutrinos are not electricallycharged. So, this force cant be either the strong force, or electromagnetism; it must be anew force, called the weak force. The force is weak because it is much weaker than eitherthe electromagnetic or strong force. The weak force is also a short-range force, operating on

even shorter distances than the strong force!Finally, we come to perhaps the most familiar of all forces - gravity. Newton told us thatanything with mass gravitates. Einstein later told us that energy and mass are equivalentsince E = mc2. So, this suggests that anything with energy gravitates, which is a directprediction of Einsteins General Relativity, as well discuss in detail later. This is a uniqueprediction of Einsteins theory, differing from Newtons theory of gravity. According toNewton, light, which has no mass, should not be affected by gravitational fields. Einsteinsays that, because it has energy, light should be affected by gravitational fields. It has been

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found that light from distant sources is deflected gravitationally around massive objects(such as galaxies) through gravitational lensing, which well discuss in detail later. Thisgives evidence for Einsteins theory. Gravity interacts between any systems that have energy,including gravity, itself - gravity gravitates! This property of nonlinearity makes problemsinvolving gravity very difficult to solve exactly, as well discuss later.

These are the four known fundamental forces. All other forces can be understood in termsof these forces (particularly electromagnetism). We would like to try to understand theseforces at a deeper level. The classical interpretation of forces is that sources set up fieldsin the surrounding space (for example, electric or gravitational) that other objects respondto, accelerating in response to these forces. Quantum mechanics changes the interpretationsomewhat. Upon applying quantum mechanics to the electromagnetic field, for example, onefinds that it is made up of a large number of photons, the individual quanta of light. Becausethe electromagnetic force is transmitted via the electromagnetic field, we are then led tobelieve that the electromagnetic force is carried by photons. That is, electric charges interactvia the exchange of photons. We would say that the photons mediate the electromagneticforce.

This idea has proven to be most useful in particle physics, and the modern viewpoint isthat all of the forces are transmitted via the exchange of different bosonic mediator particles.As weve discussed, the electromagnetic force is carried by spin-1 photons, which couple toelectric charge. This means they interact with (are absorbed and emitted by) electric charge.The photon, itself, is not charged, and so photons dont interact with each other (at leastto a first approximation). This means that electromagnetism is a linear theory, obeying theprinciple of superposition. This makes it the easiest of the forces to understand and compute.

The fundamental theory of electromagnetism is called Quantum Electrodynamics (QED).It was the first theory of the forces to be understood in a deep way, and is the pride and

joy of theoretical physics, obtaining extremely accurate results which agree precisely with

experiment to many decimal places. There has never been a prediction of QED which didnot agree with experiment.

The interaction of electric charges via the exchange of photons can be visualized in a verynice manner using a method developed by Richard Feynman, seen in the Feynman diagramin Figure 4. In this diagram, time runs along the vertical axis, while space runs along thehorizontal. This diagram represents the simplest interaction of two electrons (the straightlines labeled e), by means of a photon (the wiggly line labeled ). This is only the first-order diagram; there are, in fact, an infinite number of increasingly complicated diagrams.All of the diagrams must be added together to obtain the final answer.

It seems like this would be an impossible task, adding up all of the different diagrams.However, there is a bit of good luck, since more complicated diagrams contribute less to

the final answer. One finds that the first few (relatively easy to calculate) diagrams tell themajority of the story. QED (as well as each of the forces described below) is a beautifultheory, which we unfortunately do not have time to discuss properly; details may be foundon any book on particle physics or quantum field theory.

We have discussed the electromagnetic force from the modern viewpoint, but this is onlyone of the fundamental forces. Can we explain the other three in a similar way? Letsstart with the strong force. We also need to have the quarks interact by exchanging somesort of particle. The strong force holds the quarks together inside the protons or neutrons

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e

e

e

e

Figure 4: The Simplest Electromagnetic Interaction.

(the nucleons), and this force leaks out of the nucleons just a little bit, holding the nucleustogether. So, the force acts like glue, binding the quarks together. For this reason, the

messenger particles have been called gluons, and there are eight of them! This is to becontrasted with the photon, for which there is only one. The gluons couple to a generalizedcharge called color charge. This charge has nothing to do with real color, but is instead thequantity defined in analogy with electric charge which couples strongly-interacting particlesto the gluons.

The equations describing the quantum theory of the strong force, called Quantum Chro-modynamics, or QCD, are a bit more complicated than those of QED, and are not fullyunderstood. However, one can perform calculations using Feynman diagrams for QCD, likethose seen in the first-order diagram in Figure 5, which represents the interaction of an upquark with a down quark, exchanging a gluon. In this case, however, the summation of

the diagrams is not so simple, since higher-order diagrams contribute about as much as thesimpler ones.

u

u

ga

d

d

Figure 5: The Simplest Strong Force Interaction.

Thats two forces down - what about the weak force? Once again we postulate that theforce comes from the exchange of a particle. Beta decay proceeds due to the weak forceand has a negatively-charged down quark becoming a positively-charged up quark, with the

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emission of a negative electron and neutral particle. Although the total charge was conservedin this process, the charge of the initial and final quarks was different. This means that themediator particle is charged. We can draw the (simplest) Feynman diagram for this decayin Figure 6. The particle, technically called a vector intermediate boson, is usually justcalled a W particle. In this process, the W must be negative, with the same charge as the

electron.

d

u

W

ee

Figure 6: The Simplest Weak Force Interaction.

We also have another difference in this diagram in that the arrow for the antineutrino isrunning from top to bottom; in other words, it seems to be running backward in time! This isactually a convention, where an antiparticle may be viewed as a regular particle propagatingbackwards in time. This is completely consistent with all ideas of causality and poses noproblem - its only a convention.

Beta decay is not the only possible weak interaction. For example, a muon neutrino can

interact with a down quark, producing a muon and an up quark. The neutrino carries noelectrical charge, and so this interaction could not go via photons (also, photons dont changethe type of particle). The neutrino starts off neutral, and then becomes a negatively-chargedmuon, while the negatively-charged down quark becomes a positively-charged up quark. Theneutrino had to lose a +1 amount of charge to the down quark. This means that we need apositively charged mediator particle, W+.

Finally, there are still more interactions which preserve the electric charge (often calledneutral currents) and are mediated by still another messenger particle, called Z0. So,altogether there are three different messenger particles. The weak bosons also have anothervery interesting property compared to the other force mediators: they are massive! The W

particles have a mass equivalent to roughly 80 protons, while the Z0

has a mass of roughly92 protons. This property actually caused some theoretical difficulties in trying to formulatea quantum theory of the weak interactions, and was only satisfactorily solved by mergingthe weak and electromagnetic forces into a single electroweak theory which is discussedbelow.

Finally, we come to gravity. One would like to try to formulate a quantum mechanicaltheory of gravity, in analogy with QED, as has been done with the other forces. We can drawthe simplest gravitational Feynman diagrams, like that in Figure 7, coupling the energy of

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two particles to a gravitational messenger particle called a graviton; energy is the chargeof gravity. Unfortunately, when we try to do this we immediately run into problems.

At energy scales currently available in particle accelerators, quantum gravitational inter-actions are infinitesimally small, with the ratio of the gravitational to electric forces betweentwo protons FG/FE 10

38. However, the strength of forces actually change depending on

the energies available. In the case of gravity, the interactions actually become stronger athigher energies. At the Planck energy, EPlanck 10

18 GeV, it is expected that gravity willbecome the dominant interaction. This is important for understanding systems in whichquantum gravity is important, such as black holes and the initial Big Bang singularity. Atheory of quantum gravity contains numerous conceptual issues which have not been satis-factorily overcome, and the graviton remains experimentally undiscovered. However, as longas we limit the energy densities of our investigations to scales smaller than the Planck scale,quantum gravitational interactions are expected to be negligible. As we will see, inflation-ary dynamics will often take place at sub-Planckian scales and hence will be describable byGeneral Relativity.

T(1)

T(1)

h

T(2)

T(2)

Figure 7: The Simplest Gravitational Interaction.

Continuing our list of the particles populating the Universe, we have the different forcemediator particles in Table 3, including the spin (in units of ), the relative interactionstrength (normalizing the strong force to unity), and the effective range of the force. The fourforces appear to be very different, but it is the hope that these forces may turn out to actuallybe just different aspects of the same Unified Force, in much the same way as electricityand magnetism are not two separate forces, but really are just different manifestations ofthe same electromagnetic force. This hope has already been partially realized when the

electromagnetic and weak forces have been unified in the electroweak theory at energy scalesabove roughly 100 GeV. There is some theoretical evidence that the strong force might mergewith the electroweak force at energies of about 1016 GeV to a single Grand Unified Theory,(GUT) but the current experimental range of particle accelerators is far too low to confirmthis. Finally, there is some expectation that all of the forces might be unified at the Planckscale, but this is still unknown at present.

We can already see that there are lots of particles in the Universe! We have the quarks, theleptons, and the messenger bosons. All of these particles (except the graviton) are part of the

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Force Mediators.

Interaction Particle Spin () Strength Range (cm)

Electromagnetism Photon, A 1 1/137 Weak Force W, Z0 1 105 1016

Strong Force Gluons, ga 1 1 1013

Gravitation Graviton, h 2 1038

Table 3: The Force Mediator Particles.

Standard Model of Particle Physics, which also includes one more particle, called the Higgs.The Higgs is thought to be the origin of mass by interacting with the the other particles whichare initially massless. The Higgs is theoretically predicted, but remains (as of this writing)the last part of the Standard Model that has yet to be found experimentally. However, withthe construction of the Large Hadron Collider (LHC) there is every expectation that theHiggs will be found.

Furthermore, each of these particles has an associated antimatter partner (although insome cases the particle is its own antiparticle, as the photon is). Antimatter was originallypredicted in Diracs relativistic theory of the electron, and then was extended to all theparticles. The antimatter partner for the electron is the positron, and was discovered first.All the rest of the antimatter are simply called the anti-particle, for example the antiproton,the antineutrino, etc. When a particle and its antiparnter interact, they mutually annihilate,producing new particles. In the case of an electron and positron reaction, the most commonproducts are two gamma rays (two being required by momentum conservation), but otherproducts are possible, depending on the initial energies of the particles.

With the exception of the graviton (and also the Higgs, though possibly for not much

longer), all of the particles listed above have been discovered experimentally. Modernhigh-energy physics theories also contain more speculative ideas including supersymmetry(SUSY), which relates bosons and fermions. SUSY predicts that every boson has an associ-ated fermionic partner, while every fermion has an associated bosonic partner, doubling thenumber of particles in our list above. Supersymmetry has not been found experimentallyeither, but there are high hopes for finding supersymmetric particles at the LHC. The inclu-sion of SUSY provides even better evidence for GUTs, with the unification becoming muchmore exact. There is also hope that SUSY might provide a possible explanation for darkmatter, which well discuss below.

There are even more speculative idea emerging from string theory, which postulates thatparticles are actually tiny vibrating bits of string. Depending on whether the stringswere open or closed loops, and depending on how the strings vibrate, one obtains differentparticles. In this way unification is achieved since all the particles come from the samefundamental string. String theory also naturally includes not only SUSY, but also even thegraviton - string theory is a natural theory of gravity! String theory also predicts that theUniverse contains extra spatial dimensions, leading to a total of 10 or 11, depending on thetheory. These extra dimensions are often taken to be rolled up into tiny little shapes unde-tectable by current accelerators. Conversely, the extra dimensions could even be infinitely

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large, but our Universe could be confined to a 3-dimensional slice (or brane) of the extradimensions, rendering them unobserved.

String theory also provides possible answers for some other questions including whythe forces appear to be so different in scale, which is the so-called hierarchy problem.Overall string theory appears very favorable, holding out the possibility of being a Theory

of Everything, (TOE). Unfortunately, the ideas are very speculative, and are unlikely to beexperimentally verified for a very long time. This stems from the tininess of the strings, whichare 1033 centimeters, or so, which is far below current (or even projected) experimentalscales. If string theory is correct, it is likely to be unobserved for a very long time (althoughthere are some indirect observations which would lend credence to string theory).

We have quite a list of particles - a good theory of the Universe should explain wherethey came from!

1.0.5 The Universe Doesnt Have Any Bad Things.

According to Maxwells equations of electrodynamics, electric charges come in single units

(called monopoles), but magnetic fields come from electric currents. These currents alwaysproduce a north and south magnetic pole; there is never just a magnetic north pole with-out the corresponding magnetic south pole (and vice-versa). Maxwells equations explicitlyforbid any magnetic monopoles. However, it is not at all difficult to reformulate Maxwellsequations to include magnetic monopoles. The only reason that they do not include themis because magnetic monopoles have not been found, experimentally. However, there aremany speculative theories of physics which do include magnetic monopoles. In fact, Diracoriginally predicted that, if monopoles did exist, then it would explain why electric chargeis quantized. Furthermore, GUTs often predict that monopoles will be produced at highenergies. If monopoles do exist in the Universe, then they must be in such small numbersthat we never see them.

Einsteins General Relativity allows for a particular type of object called a cosmic string.A cosmic sting is a very dense, one-dimensional string-like object, under tremendous tension,which would produce an interesting gravitational effect. The actual gravitational attractionof an extended cosmic string is, in fact, zero! However, the string has an effect on thesurrounding space, leading to a deflection of light around the string. Because gravitationallensing is seen regularly in astronomical observations, one can place limits on the number ofcosmic strings in the Universe, and current observations have found none.

Magnetic monopoles and cosmic strings are examples of topological defects. A topologicaldefect is formed during a phase transition in the early Universe. Phase transitions are familiarfrom when ice melts into water, for example, when the state transforms from one state to

another. Phase transitions in the early Universe involve the Universe transitioning from onevacuum state into another as it cools, breaking a symmetry in the theory. The electroweaktheory does the same thing, splitting the fundamental quanta of the electroweak theory intothe photon and W and Z0 particles; a more symmetric system has broken down into a lesssymmetric system via a phase transition.

Another example of a topological defect may be found in a ferromagnetic material, likeiron. A magnetic domain is a region of a magnetic material in which all the magneticmoments line up and point in a single direction. A magnetic material is made up of a large

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number of these magnetic domains, and each domain is separated from the other domainsby a domain wall. The domain wall is the topological defect, separating one magneticdomain from another.

Topological defects formed during phase transitions in the Universe come in several differ-ent varieties, which weve actually discussed already. Zero-dimensional topological defects are

the magnetic monopoles, one-dimensional defects are the cosmic strings, and two-dimensionaldefects are domain walls. Observations have not shown any of these objects, but GUTs oftenpredict that they should exist. Again, if they do exist then their numbers should be verysmall.

One might include antimatter in the list of bad things that we dont see since theUniverse seems to have so much more matter than antimatter. However, we do actuallysee some antimatter occurring naturally. The question of why we see so little antimatterrelative to matter is still unanswered, but it is thought that the mechanism that producedmatter and antimatter in the early Universe produced a very slight excess of matter. Forevery billion particles of antimatter produced there were about a billion and one of matter.The antimatter annihilated with the matter, leaving only the excess matter particles whichthen populated the Universe. So, although naturally-occuring antimatter in bulk is rare, itis not a bad thing.

A good theory of the Universe should not only explain where the good things come from,but also why we dont see any bad things!

1.0.6 There Are Dark Things.

Our discussion of the constituents of the Universe actually leaves out two pieces (that weknow about) The identity of these pieces are completely unknown, but they provide veryinteresting effects which well discuss now. Due to the still-mysterious nature of these piecesthey are called dark, and are dark matter and dark energy. Well start with dark matter,and then discuss dark energy in the next section.

Observations of galaxies have shown some very peculiar behavior. If we count up thevisible stars then the majority of the stars lie near the center of the galaxy, with the stellardensity decreasing as we move outward. Thus, most of the mass should be concentrated inthe center. Since gravity gets weaker as we move away from a mass, the outer stars shouldmove at a different rate in their orbits than do the stars closer to the center. Simply settingthe Gravitational force law, FG = GMm/r

2 equal to the centripetal force FC = mv2/r

suggests that the stars should move with speeds v =GM/r, where r is the distance from

the center. In other words, the stars further out from the center of the galaxy should movemore slowly than do those closer to the center, in exactly the same way that planets more

distant from the Sun move more slowly than those closer to the Sun.Careful observations, beginning with Zwicky in the 1930s, show that the velocity does

not fall off with distance! In fact, the speeds tend to approach a constant value as theradius increases. What this suggests is that the matter in a galaxy is not concentrated inthe center, but is rather dispersed throughout the galaxy (extending even past the visiblestars). In order for the velocity curve to go to a constant at large distances we would needthe mass to increase as we move out, i.e., M r.

We can explain the different speeds by immersing the visible galaxy in a large roughly

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spherically-symmetric cloud of massive particles, also called a halo. As is well-known, thegravitational force on a mass inside a material is different from the force from a point mass;for example, inside a constant density cloud, the gravitational force is proportional to thedistance away from the center. In order for the mass to be proportional to distance, thedensity of these particles needs to fall off as r2 at large distances, concentrating the

particles near the center. These hypothetical particles are called dark matter, where darkmeans that it doesnt interact electromagnetically, and so doesnt emit light.

This discussion on galactic rotation rates relied very heavily on the correctness of Newto-nian dynamics at large distance (galactic) scales. Shouldnt we have used Einsteins theoryof gravity? For these distance scales, it turns out that Newtonian gravity is a good enoughapproximation such that it is perfectly fine to use it. General relativity is really only neededon very large distance scales (say megaparsec scales), or when the gravitational fields areextremely strong, as in black holes; the dynamics here are well-described by Newtoniangravity.

However, we find very different behavior for the galaxy rotation rates than we expect,based on Newtons theory of gravity. We have attributed it to a dark matter particle, butone might wonder if the dynamics might be due, instead, to the modification of Newtoniangravity on large scales. If Newtons theory of gravity changes from the usual inverse-squarelaw, becoming instead FG 1/r at large distances, then the galactic rotation curves willhave the observed behavior.

A possible modification of gravity is called modified Newtonian dynamics, or MOND,and has been considered for some time. MOND was considered a serious contender to theparticle theory of dark matter for quite a while, but then a very interesting observation wasmade of the Bullet cluster [4]. The Bullet cluster is a system of two colliding clusters ofgalaxies, as seen in Figure 8.

Figure 8: The Bullet Cluster shows the best evidence for dark matter particles.

During the collision, most of the stars miss each other, but the gases comprising thegalaxies interact electromagnetically leading to friction and therefore heating to temperatures

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of around 107 Kelvins. Upon heating the gases emit X-rays, which are seen as the pink areasof the image (the galaxies are seen optically in the picture, as well). The gases are comprisedof the usual baryonic matter and account for the visible matter in the galaxies. The blueareas show the distribution of mass in the system via gravitational lensing. Notice that thepink and blue areas overlap only slightly, meaning that most of the matter comprising the

galaxy is not emitting X-rays, and so is dark.Due to the frictional slowing caused by both electromagnetic and gravitational interac-

tions, the baryonic matter moves slightly more slowly than the non-baryonic matter whichinteracts only gravitationally at these large distance scales, leading to the separation of pinkand blue. According to MOND the hot gas is still the most massive component in thegalaxies, and so the gravitational lensing effect would be centered on the gas, leading to noseparation between the pink and blue areas. Observationally, the Bullet cluster seems torule out MOND as a viable theory, enforcing the we need for a dark particle, which infact comprises the majority of matter in the Universe. It is expected that the dark matterprovides the initial seeds for structure (like galaxy) formation in the early Universe, as wellas contributing to anisotropies in the CMB.

Now, the question is what is the dark matter particle? There could be all sorts of dif-ferent contributions to the extra mass of the galaxies. For example, neutrinos seem to fit thebill, since they dont interact electromagnetically. However, neutrinos are nearly massless,and so move at highly relativistic speeds which would not allow them to clump togetherunder their mutual gravitation. If the dark matter in the early Universe (called primordialdark matter) provided the initial gravitational seeds to form galaxies, then neutrinos couldnot help. While neutrinos might contribute some amount to dark matter, this relativistic(hot) component must contribute only a small amount.

We thus expect dark matter to be cold, or non-relativistic. This means that the darkmatter particles will be massive, since heavy particles dont move as fast, and so will tend

to clump together gravitationally. As we will discuss later, the very early Universe wasextremely hot, which provided plenty of energy to create particles of every type. Some ofthese particles annihilated or decayed, and the leftover ones (including dark matter) filled theUniverse. If the particles decayed too fast or too slowly, then we wouldnt get the observeddark matter density. It turns out that if the particles interact via the weak force then thedark matter density comes out right. If the particles interact either electromagnetically(which is already ruled out since we dont see any light coming from them), or strongly thenthe decay rate is too fast. If the particles only interact gravitationally then the decay rateis far too slow; weak seems just right, predicting the correct relic abundance of dark matter.

So, we expect the dark matter particles to be weakly-interacting massive particles (WIMPS).There are no good candidates in the Standard Model of particle physics, but the more spec-

ulative theories (particularly SUSY) provide excellent candidates. The lightest superpartner(LSP) is stable, protected by a particular symmetry (called R-parity), and having nolighter superparticles to decay into, and provides a possible dark matter candidate. Themost likely superpartner is called the neutralino, , and is actually a mixture of the super-partners of the Z boson, the photon, and the Higgs particle. String theory also predicts aninfinite number additional particles (called a Kaluza-Klein or KK tower), of ever increas-ing masses. These particles also have the potential to describe dark matter, but are morespeculative than even SUSY.

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So, we see that observations require the existence of a brand new particle, so far undis-covered by experiment. However, this is not the only unexpected observation that has beenfound. Observations in the early 20th century found that distant galaxies are moving awayfrom us with a speed depending on their distance. This led to a fundamental understandingthat the Universe is expanding, suggesting that it has a finite lifetime. This surprising ob-

servation was compounded in the late 20th century with the additional observation that therate of the expansion is actually accelerating! Physics is now faced with the non-trivial taskof explaining where this acceleration is coming from and leads to the idea of dark energy, towhich we now turn.

1.0.7 The Universe is Expanding!

Looking out at the night sky, we see a blanket of stars which seems unchanging, and it wouldbe natural to expect that the Universe has always been as we see it. However, this actuallyleads to several apparent problems. Among the first to be thought up, known as Olbersparadaox, asks why the night sky is dark. Olber suggested that if the Universe was infinite

and uniformly distributed with stars, then any line of sight should end on a star. Thereforethe night sky should be as bright as the daytime sky. One might think that the starlightcould be absorbed by intervening dust and gas, but this doesnt solve the problem. The dustwould absorb the starlight and heat up, eventually reaching the same temperature as thestar and re-radiating the light to us.

One possible way out of Olbers paradox is that the stars turned on at some point in thepast, and this is the case. Well return to this discussion below, but it turns out that thereis an even bigger problem. If the Universe was infinite and uniformly distributed with stars,then it could form a static gravitational system. The stars wouldnt collapse towards thecenter of mass, since there would be no center of mass to collapse to! However, this systemis extremely unstable, like a pencil balanced on the tip. Any slight perturbation of the stars,pushing two any closer to each other by even a small amount would lead to a gravitationalinstability. The two stars would attract, moving together, leading to a single area of greatermass. This causes some stars to collapse together, while others drift apart. This leads to arunaway gravitational collapse which would eventually lead to a sky devoid of any stars atall, save perhaps for large collections of them in individual areas.

The answer of whether the Universe is static or evolving was finally answered only nearthe start of the 20th century, and was done by observing the light from distant galaxies.Since the stars in these galaxies are the same, overall, as the stars in our own, we know whatsort of light we should expect to see. However, upon looking at this light we see that it is notquite right; the light from the most distant galaxies is redder than we should expect. The

explanation for this may be found in the familiar Doppler effect: we know that light emittedfrom a source moving away from us has its wavelength stretched out, leading to a redshift.A source which is moving towards us would have its wavelength compressed, leading to ablueshift. This means that the distant galaxies are moving away from us!

This discovery was made by Hubble in the 1920s, and Figure 9 shows his plot of reces-sional velocity of the galaxy, versus the distance to that galaxy, in megaparsecs [5]. Thereis a very clear dependence of velocity on distance, leading to a linear relationship, v d.Hubble was the first to note this relationship, which has since been called Hubbles law.

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Well discuss Hubbles law in detail later; for now, its enough to realize that the Universe isexpanding.

Figure 9: Hubble found that the Universe was expanding, as seen here in his original plotfrom 1929.

Einstein originally believed the Universe to be static, but he knew of the problems withstability. Therefore, when he applied his theory of gravity to the Universe, he tried to add anadditional constant term to his equations that could provide a repulsive force, counteractingthe collapse. When Hubble discovered the expanding Universe, Einstein no longer saw aneed for the new term and banished the cosmological constant from his equations, calling ithis biggest blunder. For the better part of a century, this term was believed to be zero,

but everything changed in 1998 when two teams of astronomers looked at distant type Iasupernovae [6, 7].

Type Ia supernovae occur in binary star systems where a white dwarf accretes materialfrom a nearby red giant star. The mass of the white dwarf increases until it reaches about 1.4solar masses. At this point, called the Chandrasekhar limit, the white dwarf can no longersupport itself via electron degeneracy pressure (an effect of the Pauli exclusion principle)against gravity and it begins to collapse. The gravitational collapse raises the temperatureof the white dwarf fusing heavier elements in the core until iron is reached.

Once iron forms in the core, it takes more energy to fuse it than is released in the fusionprocess. The core then begins to gravitationally collapse forming neutrons, which then resistfurther compression via neutron degeneracy pressure. This resistance leads to a rebound

effect, creating an outward shockwave. By a process that is still not completely understood,this shockwave acts with other processes (involving neutrinos, for example) to blow awaythe outer layers of the white dwarf in a tremendous explosion (which, in some cases, blowsthe companion red giant star away). For a brief while the supernova explosion is brighterthan all the rest of the stars in the galaxy combined (see Figure 10)!

Because the mechanism of type Ia supernova is so regular, occurring when the massreaches the Chandrasekhar limit, the explosion has a characteristic power released (calledthe luminosity), which waxes and wanes in a predictable manner. This intrinsic luminosity

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Figure 10: Hubble Space Telescope Image of Supernova 1994D in Galaxy NGC 4526 [8].The very bright spot, outshining all the rest of the stars in the galaxy, is a single star goingsupernova!

leads to a specific brightness (apparent magnitude) at a specific distance, falling off inversely

as the square of the distance to the supernova. So, if we measure the distance to thesupernova, then we can determine the distance. Objects of this type, in which the distancecan be inferred from measurements of the brightness are called standard candles, and areamong the most important distance measurement techniques in astronomy.

In 1998 two teams of astronomers looked at dozens of type Ia supernovae. They knew thatthe Universe is expanding, and it is expected that gravity should be slowing that expansionrate, just as gravity slows the rise of a ball thrown in to the air. The teams set out to measurethat rate of slowing. Because the Universe is expanding, light from distant supernovae shouldbe redshifted, just as is the light from distant galaxies, which we can also use as a methodfor determining distance. If gravity is slowing down the expansion, then the light that wesee should be brighter than we should expect based on the redshift. This is because the

light was emitted from the supernova at some point in the past. The wavelength of the lightis stretched out on its way to us by the Universal expansion, and depends on the speedthat the supernova had when the light was emitted (i.e., the speed of the expansion in thepast). However, the brightness that we see depends on the distance that the supernova isnow, because the light is spread out over a spherical surface area (this is just the flux law,required from conservation of energy). If the expansion rate is slowing down due to mutualgravitational attraction, then the supernova would appear to be moving faster, based onthe redshift, and we would expect that the distance to them is smaller than it would be if

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the rate was constant. So, since the distance is smaller than we would expect based on theredshift, the supernova would look brighter than we would expect, if we use the distancegiven by the redshift. So, if the Universe is slowing down its rate of expansion, then thesupernova would be brighter than expected. This difference in brightness is exactly what thetwo teams set out to measure.

When the astronomers actually made the measurements, they found that the supernovaewere, in fact, dimmer than they were expecting! This implies that the Universal expansionrate is speeding up; the Universe is expanding faster today than it was yesterday! This iscompletely contrary to the expected result; it means that there must be some sort of agent,resisting the gravitational collapse, accelerating the Universes expansion. The question nowis, what is it?

This unknown whatever-it-is has been called Dark Energy, but this is only a name forour ignorance. While there are many theories, the identity of dark energy is still completelyunknown. The currently prevailing theory, however, is that dark energy could be Einsteinsold nemesis, the Cosmological Constant.

The Cosmological Constant (CC) fits the bill, giving a repulsive force acting on mega-parsec scales. Furthermore, it also has a very straightforward interpretation coming fromquantum mechanics: it is the energy of the vacuum! Remember the uncertainty principle,which says that you cant know the exact energy of a system to arbitrary accuracy. Thisuncertainty leads to fluctuations in the energy about its ground state (called zero-pointfluctuations), which are most familiar in the quantum mechanical harmonic oscillator. Eachoscillator carries a zero-point energy, 1

2, which contributes to the overall energy of the

system. Adding the contributions from all the different frequencies gives an infinite energy.Typically this is not actually a problem; just as only differences in potential energy is

physically relevant, so too is the case here. The infinite vacuum energy sets the background,against which all other energies are measured. Since only the differences are important,

one can rescale the energy, subtracting away the infinite contribution. However, one finds aproblem when applying this idea to gravitation. Einstein tells us that mass and energy areequivalent, and so anything with energy gravitates. This means that the infinte backgroundshould create an infinite gravitational effect!

There are artificial ways out of this problem. For example, in exact supersymmetry onefinds that the total vacuum energy is precisely zero, with the contributions from all theparticles being canceled by contributions from their superpartners. However, we dont seeSUSY at everyday energies, and so it is a broken symmetry, which will then give a vacuumenergy. The vacuum energy obtained upon the breaking of SUSY then looks to be againinfinite.

One might suggest that we dont get contributions to the vacuum energy from all of

the frequencies, but rather only up to a certain cutoff frequency, beyond which our theorybreaks down. In this case, the infinite effect becomes finite, which can be dealt with. Thismeans that our theory is no longer fundamental, but only an effective theory, which workswell below the cutoff scale, but fails above it. Above the cutoff scale, one needs the trulyfundamental (but unknown) theory (often called the UV completion of the theory) to whichthe effective theory is only an approximation. A familiar example of this is Special Relativityreducing to Newtons laws at low speeds.

The problem with this idea is that the natural cutoff is of the order of the Planck energy,

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or about 1018 GeV, which gives a CC so large that the Universe would immediately haveblown itself apart! Upon performing this straightforward calculation, one finds that theobserved value of the CC is 10120 of the theoretical result; i.e., it is zero for 120 decimalplaces, and then nonzero! This wildly differing expanse between theory and experimentis called the Cosmological Constant Problem, and has been called the Biggest Mystery in

Physics. Why is the CC so small? It is the job of modern theoretical physics to answerwhy the CC is not infinite (as predicted by quantum mechanics), and not precisely zero (aswould be the case with unbroken SUSY), but instead the tiny value that it is.

One particular area of interest regarding the Cosmological Constant asks is it really aconstant? The simplest description of dark energy is a constant vacuum energy, taking thesame value everywhere in the Universe. However, as we will see, there are other objects thatcan mimic a CC; for example a slowly-varying scalar field can approximate the effect of aCC to arbitrary accuracy. Because dark energy is so completely unknown, the observationalproperties of the Universal expansion are a subject of great theoretical interest. If it is foundthat the rate of acceleration changes with time, then one can rule out a CC, and proceed toeven more interesting explanations.

As has already been discussed, the Universe is spatially flat. This flatness tells us some-thing about the density of the Universe. If the density was too large, then the Universe wouldrecollapse at some point due to mutual gravitational attraction, regardless of the small Cos-mological Constant - the Universe is closed. If the density is too small, then the CC takesover and blows the Universe apart at an ever-increasing rate, leading to an open Universe.If the density is critical (just right), then the Universe expands forever, but asymptoting toa finite acceleration. This behavior is analogous to the escape velocity of a projectile. If theinitial velocity is too small then the object is pulled back to Earth, in analogy with a closedUniverse. If the initial velocity is larger than escape, then the projectile escapes with extravelocity, as in an open Universe. When the projectile is fired at escape velocity, then it just

barely escapes with no extra speed, as in the critical (flat) Universe case.The flatness places constraints on the total density of the Universe, telling us that the

density is extremely close to critical. Since the total density is determined by the densitiesof the individual components (ordinary or baryonic matter, dark matter, and dark energy),the densities must add up to critical. Weve already seen that there is far more dark matterthan baryonic matter, and so the dark matter density will contribute more. Finally, onlarge scales the dark energy is the important part, and so we expect that the dark energydensity will also be important. Observations from the redshift of supernovae have placedfairly precise values on each of these densities. We now know that the Universe is made upof about 4% baryonic material, 23% dark matter, and about 73% dark energy; the majorityof the Universe is not only dark, but completely unknown as well! As we will see later, which

component of the Universe (matter, or dark energy) dominates, and describes the subsequentevolution, changes as the Universe evolves, with dark energy becoming important only atlate times. This completes the mosaic of the Universe.

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2 How Did It Get That Way?

We now have a very good picture of the Universe, even though the majority of it is completelyunknown. We now need to consider what this picture tells us about the evolution of theUniverse and how it came to be in such a state. As we will see, the attempt to answer this

question leads to some new questions. At first glance, it would appear that the Universecould only have evolved from a very finely-tuned beginning; generic initial conditions do notlead, at all, to what we see in the sky. Furthermore, it turns out that some of the conditionsare not only unlikely, but also impossible under the standard picture of Universal expansion.We will return to these problems after we get an idea of where the Universe came from.

2.1 The Big Bang

Weve seen that the Universe is expanding; distant galaxies are flying away from us with aspeed proportional to their distance away. This means that the galaxies were closer to usyesterday than they are today, and closer, still, a million years ago. Lets run the expansion

backwards as far back as we can. Eventually all of the galaxies would have been on top ofeach other. Further back and all the stars would have been in the same place. Keep rollingthe film backwards and everything would have been at the same point. We are thus ledto believe that the entire Universe exploded from a single point! The Universe has beenexpanding ever since, carried along by the energy of the explosion. This explosion has beencalled the Big Bang.

The Big Bang model provides an excellent explanation for the Universe. It explainswhy the galaxies are flying apart. It also explains where all the stuff in the Universecame from. The initial energy of the Big Bang was extremely high (effectively infinite),and some of this energy went into the expansion, while the rest of it goes into the creation

of matter (via E = mc

2

). At first, lighter constituents were formed, such as photons,neutrinos and quark-antiquark pairs (the pairs being required to conserve charge). Thematter and antimatter annihilated, leaving a slight excess of matter populating the earlyUniverse. Different quarks paired up into protons and neutrons, which then combined intomostly hydrogen, plus a smaller amount of helium via primordial nucleosynthesis. Muchlater, these primordial elements collapsed gravitationally into stars. Furthermore, becausethe initial energy of the explosion was so great, and since temperature is just a measure ofthe energy of a system, we can even understand the 2.73 Kelvin background temperature ofspace as expansive cooling. Just as a gas-filled piston cools down as the volume is increased,so too does the Universe. Tracing the expansion of the Universe back places a lifetime ofroughly 13.7 billion years, which well discuss later.

But, were still not done; we can also explain the cosmic microwave background (CMB).Right after the Big Bang, the density of the Universe was extremely high. The tiny Universewas filled with charged particles that scattered photons back and forth between them, inexactly the same way as a cloud scatters the light. Just as a cloud is opaque, so too wasthe early Universe! About 379,000 years after the Big Bang, the density dropped enoughsuch that the photons dont easily find a charged particle to scatter off of and they startfreestreaming (this is the same reason why a cloud has a visible edge). The Universe becametransparent to visible light, and the CMB photons have been traveling to us ever since. This

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is why the CMB has been called the afterglow of the Big Bang.The photons were initially very high-energy, but have had their wavelengths stretched

by the Universal expansion, and are now in the microwave range. The CMB is the farthestback in time that we can see optically, but because neutrinos interact weakly, they startedfreestreaming much earlier than the photons. There is the hope that neutrino astronomy

could allow us to see further back, but the difficulty in detecting neutrinos has so far renderedthis intractable (in fact, gravitational waves would elucidate still earlier times, but they havenot been detected, yet).

We can see that the Big Bang model seems to work very well. There have been otherattempted explanations from time to time, such as a steady state model harkening backto the static Universe idea, but these other models have not found wide support. Later, wewill see that we get precision agreement with cosmological data using the Big Bang model,augmented with the inflationary ideas.

3 A Short History of the Universe.

Now that we have a good basic idea of the evolution of the Universe, lets look at the evolutionin a little more detail. We can actually trace the history of the Universe back to very earlytimes based on the known laws of nuclear and high-energy physics. The ambient temperatureof the Universe needs to fall to such levels that quarks can form into nucleons, nucleons andelectrons can form into atoms, and so on. This gives us an idea of the background energiesand, since an energy of 1 electron volt corresponds to roughly 12000 Kelvins, temperatureswhich can be then linked to the time since the Big Bang. Lets look at some differentimportant times in the history of the Universe, listing the times, energies, and temperaturesin these eras.

t = 0 seconds. This is the Big Bang singularity, the origin of everything! The entireUniverse is crammed down into a single point of effectively infinite density. The tem-peratures and energies are also effectively infinite. This era is completely beyond theknown laws of physics!

t 1043 seconds. This is the Planck era, where the (unknown) laws of quantumgravity become important. The background energy is about 1018 GeV, giving a tem-perature of about T 1031 K. This era is still completely unknown, but if string theoryis true then string interactions should be important, here. If the four forces are unifiedas a single force, then it is at this point that gravity breaks away, leaving the otherthree forces as a Grand Unified Theory (GUT).

t 1036 seconds. The energy has dropped to 1016 GeV, with a temperature ofT 1029 K. It is thought that this could be the GUT scale, where the strong forcedecouples from the electroweak force. Topological defects (like cosmic strings) may beproduced in this breaking. This era is still resides in the realm of speculative theoriesof physics.

In the range of 1035 t 1014 seconds, the energies drop from 1016 GeV to 104

GeV, while the temperatures drop from T 1029 to T 1017 K. This entire range

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is still outside of the reach of current particle accelerators (although the lower limit isjust reachable at the LHC). In this region, the electric and weak forces are still unifiedas the electroweak theory. If supersymmetry (SUSY) exists, then it is very likely to bebroken during these times. It is also expected that a period of accelerated expansion,called inflation, occurs during this time (perhaps at around t 1034 seconds). The

investigation of inflation will form the majority of our work.

t 1010 seconds. The energy has dropped to 103 GeV, or one TeV, and the tempera-tures have fallen to T 1016 K. This range is right at the edge of current accelerators.SUSY has broken, and below these energies the electroweak force has split into elec-tromagnetism and the weak force.

t 105 seconds. The energy is now at about 100 MeV, and the temperatures areabout T 1012 K. The background quark-gluon plasma has cooled down enough forthem to form baryons (such as protons and neutrons) and mesons (quark-antiquarkpairs) in a way that is still not completely understood. However, the temperatures

are still too high for the nucleons to bond to form any more complicated nuclei (likehelium). The energy is now low enough that baryon-antibaryon pairs no longer form(allowing net annihilation of the pairs), but there are processes that keep the numberof protons and neutrons in roughly equilibrium. The tiny baryon-antibaryon asymme-try now comes into effect, leading to the slight excess of baryons after the particle-antiparticle annihilation.

In the range 0.01 t 0.1 seconds, the energy drops from roughly 10 to 1 MeV. Thetemperature is now T 1010 K. In this range the weak interactions fall out of equi-librium since particles are getting further apart, and so neutrinos start to freestream.Furthermore, the processes that keep the number of protons and neutrons in equilib-

rium also fall out of equilibrium, which then fix the relative numbers of protons andneutrons. The relative abundances of the primordial elements are determined by theserelative numbers of nucleons.

We finally reach t 1 second. The energy is now about 0.5 MeV, and the temperaturehas fallen to T 109 K. The energy density has dropped below the rest mass ofthe electron, which means the electron-positron pairs are not replenished when theyannihilate. Once again, the very slight excess of electrons over positrons leads to aslight excess of electrons. The temperatures are still far too high to allow the freeelectrons to merge with the nuclei to form neutral atoms, however.

At t

200 seconds the energy has dropped to about 0.01 MeV, and the temperature isnow T 108 K. At these energies the nuclear reactions become important and protonsand neutrons can form larger nuclei. Helium and other lighter elements are formedduring this Big Bang Nucleosynthesis (BBN). The observations of the abundances ofprimordial elements are in very good agreement with theoretical predictions, and forma very important check on the Big Bang theory.

Now we skip ahead to t 104 years. The energy is now at about 1 eV, and the temper-ature is T 104 K, which is below the temperature of the sun, still too high for neutral

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atoms to form. This is also the era in which the evolution of the Universe changes frombeing dominated by radiation (photons and neutrinos), to being dominated by matter.This era is called matter-radiation equality.

At at time t 105 years, the energy has fallen to energy 0.1 eV, and the temperature

to T

103

K, or roughly the melting point of lead. The temperature has fallen so thatthe free electrons can join with the free nuclei to form neutral atoms in a process calledrecombination(which isnt the best term, since the particles were never combined in thefirst place). Now that the Universe is neutral, overall, photons dont scatter as readily,and begin to freestream. The Universe becomes transparent to radiation, leading tothe cosmic microwave background (CMB). The tiny density fluctuations leave theirimprints in the CMB and are seen as the temperature fluctuations in Figure 3.

Skipping ahead again to t 108 years, the energy has now dropped to about 102 eV.The temperature is T 50 K, which is below room temperature. By this time thetiny density perturbations in the early Universe (as seen in the CMB) have provided

the initial gravitational seeds to allow for the stars to form galaxies. This begins theformation of large-scale structure.

At t 109 years, the energy is now 103 eV, and the temperature has fallen toT 5 K. Our solar system forms, giving rise to a very pretty blue-green planet calledEarth.

At t 13.73 109 years, the background energy is on the meV scales, and the tem-perature has dropped to about 2.725 Kelvins. Weve reached today!

Based on this timeline, we see that we can understand the Universe all the way back tot 1010 seconds after the Big Bang, based on experimentally-confirmed and well-known

laws of high-energy physics. Extending the time back to t 1035 seconds relies on muchmore speculative theories, but we dont expect there to be any big surprises; in particular,effects from the unknown quantum theory of gravity should not be important. This era alsoincludes the inflationary regime that will occupy most of our time in later chapters. However,going even further back towards the initial singularity stretches our understanding of thelaws of physics past its breaking point. Direct experimental evidence of the physics at theseenergies is not coming from particle accelerators any time soon, and so our understandingwill have to come from clues in the astronomical observations. It is clear, however, that weseem to have a pretty good picture of the evolution of the Universe. But now lets look a bitcloser.

4 The Big Bang Isnt Perfect!

The Big Bang picture seems remarkably good at first glance, offering us a very nice picture ofthe Universe and its evolution. However, upon closer examination we find that the Big Bangmodel doesnt quite explain everything satisfactorily; some problems creep into the theorywhich arent addressed in the standard Big Bang picture. It looks as though the Universe aswe see it today could not arise from generic initial conditions, but only very specific ones. To

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answer these problems we will need to expand the Big Band theory to include an era of notjust Universal expansion, but accelerated expansion. Lets look at some of these problemsin a bit more detail.

4.1 Problems Associated With the Big Bang

4.1.1 Initial Singularity.

The most obvious problem associated with the Big Bang is that of the initial singularity thatgave rise to the Big Bang in the first place. The theory does not address what it was thatbanged, or what caused it to bang. All the known laws of physics break down at theinstant of creation; all we can do is calculate what happens at subsequent times. It is hopedthat a complete theory of quantum gravity would solve at least some of the problems withthe initial singularity, but this will not be clear until we have that complete theory. So far,although there have been suggestions as to how to think about the Big Bang, the solutionto this problem is still unknown.

4.1.2 Flatness Problem.

As we have discussed, the Universe is spatially flat. One might ask, why does it have tobe so flat? The initial singularity had tremendous energy, and could have led to a largespatial curvature. Could the Universe have started out with a spatial curvature, but evolvedto flatness as it expands, so that it looks flat now? Unfortunately, this explanation isproblematic. We will see later that, if the Universe started out exactly flat, then it remainsso forever. But, if the Universe expands dominated by either matter or radiation then itactually evolves away from flatness as time goes on. This means that the the Universe shouldbe flatter in the past than it is now; in particular it should have started off extremely close

to flatness in the instants after the Big Bang. So, the question now becomes why does theUniverse start out so flat? The small Cosmological Constant doesnt help here, since itscontribution is subdominant to matter, and especially radiation, in the early Universe. Theflatness problem is sometimes phrased as an age problem since the spatial curvature is tiedto the fate of the Universe; Why is the Universe so old?

4.1.3 Horizon Problem.

Consider again the cosmic microwave background (CMB) seen in the whole-sky map in Figure3. The temperature of 2.725 K throughout the sky is remarkably uniform; the deviationsfrom this average are of order T/T 105. This poses a very serious problem, why

are distant parts of space so uniform? The Universe started out very hot and cooled asit expanded. But, as it expanded different parts of the Universe moved away from eachother, eventually moving so far apart that they could not communicate with each other viaexchanging light signals (they are separated by horizons). We say that they have fallen outof causal contact with each other. If this is the case, then why should they cool off in exactlythe same way? The maximum angular separation between two points on the CMB turnsout to be less than 2 degrees, which leads to some 1084 causally disconnected regions just in

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the first instant of time! So, by what means did two points at different ends of the Universecome to thermal equilibrium?

4.1.4 Initial Inhomogeneities.

An additional problem has to do with the origin of structure. One needs to figure out a wayof arranging for the initial density of the Universe to be extremely uniform, as is requiredby the CMB (the horizon problem). But then, how does one arrange at the same timefor the small deviations from homogeneity? These deviations provide the initial seeds forgalaxy formation, since perfect homogeneity would form no overdense regions to initiategravitational collapse.

4.2 How To Fix Up The Problems?

We can see that there are quite a few problems associated with the Big Bang theory. Theseverity of these problems actually varies, and depends on whether one believes that the ini-

tial conditions of the Universe should be contained in the theory describing it. For example,the flatness problem is not a problem in the strictest sense; the Universe could simply havestarted out flat from the beginning by some unknown (but not unknowable) means. Whileit is not ideal to be ignorant of the reason for flatness, there is no reason why it should notbe so, either.

Similarly, the inhomogeneity problem may only be a technical problem. Once the averagehomogeneity is explained, one simply needs to explain why this overall average deviates.This may not be that difficult, in general. As we will see, quantum fluctuations may providethe answer acting as small perturbations about the background. Already, we have some hopein this problem.

Turning to the horizon problem, however, we do find a genuine problem. Because noinformation can travel faster than light, it seems impossible that distant points of the Uni-verse should be similar to such an exacting extent. The solution might seem to require someacausal, faster-than-light, communication. But such an effect has never been seen, and isforbidden by Einsteins theory. If the Universe had existed forever, then it would have aninfinite amount of time to thermalize. But, the expansion of the Universe suggests a finitelifetime, and so there hasnt been enough time to reach thermal equilibrium. Here we cantappeal to some special initial conditions to provide the answer; we have a real paradox.

So, although the Big Bang seems to be successful in predicting the properties of theobservable Universe, it is not without its faults. We want to save the virtues of the Big Bangtheory, while at the same time fixing up the shortcomings. We dont want to throw out the

theory, but rather tweak it a little bit. This is precisely what the inflationary theory does.Inflation says that the Universe arose from a tiny region of space which expanded super-

luminally (inflated) to vast scales. During this inflationary period, the Universe is actuallypushed towards flatness, irrespective of the initial spatial curvature. Furthermore, if theUniverse started out from a tiny region, then regions that originally started off in causalcontact are blown up. This means that they could evolve in the same way, addressing thehorizon problem. The inhomogeneities in the tiny region are pushed out of the observable

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Universe, leading to an overall homogenous Universe, while tiny quantum fluctuations areblown up to the huge scales providing the density perturbations.

The previous discussion of inflation has been very quick and at a completely qualitativelevel, as has the rest of this chapter. We will spend most of the rest of our time fleshingout this basic description of the Universe. Now that weve had a nice tour of the Universe,

we need to get more quantitative to understand it. It is to this quantitative picture that wenow turn.

References

[1] The Hubble Ultra Deep image can be found on NASAs website, http://www.nasa.gov/images/content/56539main_closer.jpg .

[2] The Sloan Digital Sky Survey Galaxy Map image can be found on the SDSS site,

http://www.sdss.org/.

[3] The WMAP image can be found on NASAs website, http://www.nasa.gov/topics/universe/features/wmap_five.html .

[4] The Bullet Cluster image can be found on the Chandra X-Ray Observatory website,http://chandra.harvard.edu/photo/2006/1e0657/ .

[5] E. Hubble, A relation between distance and radial velocity among extragalactic neb-

ulae, Proc. Nat. Acad. Sci. 15, 168 (1929).

[6] A. G. Riess et al. [Supernova Search Team Collaboration], Observational Evidencefrom Supernovae for an Accelerating Universe and a Cosmological Constant, Astron.J. 116, 1009 (1998) [arXiv:astro-ph/9805201].

[7] S. Perlmutter et al. [Supernova Cosmology Project Collaboration], Astrophys. J. 517,565 (1999) [arXiv:astro-ph/9812133].

[8] The Supernova image can be found on the European Homepage for the NASA/ESAHubble Space Telescope website, http://www.spacetelescope.org/images/html/

opo9919i.html.
http://www.nasa.gov/images/content/56539main_closer.jpghttp://www.nasa.gov/images/content/56539main_closer.jpghttp://www.sdss.org/http://www.sdss.org/http://www.nasa.gov/topics/universe/features/wmap_five.htmlhttp://www.nasa.gov/topics/universe/features/wmap_five.htmlhttp://chandra.harvard.edu/photo/2006/1e0657/http://www.spacetelescope.org/images/html/opo9919i.htmlhttp://www.spacetelescope.org/images/html/opo9919i.htmlhttp://www.spacetelescope.org/images/html/opo9919i.htmlhttp://www.spacetelescope.org/images/html/opo9919i.htmlhttp://www.spacetelescope.org/images/html/opo9919i.htmlhttp://chandra.harvard.edu/photo/2006/1e0657/http://www.nasa.gov/topics/universe/features/wmap_five.htmlhttp://www.nasa.gov/topics/universe/features/wmap_five.htmlhttp://www.sdss.org/http://www.nasa.gov/images/content/56539main_closer.jpghttp://www.nasa.gov/images/content/56539main_closer.jpg

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