Lecture 24Early Universe -Testing Models

ASTR 340

Fall 2006

Dennis Papadopoulos

Chapters 12- 13

The Big Bang-Brief Introduction

• What were conditions like in the early universe?

• What is the history of the universe according to the Big Bang theory?

BACKGROUND: THE STRUCTURE OF MATTER

• Atom is made up of…– Nucleus (very tiny but contains most off

mass)– Electrons (orbit around the nucleus)– Atom held together by attraction between

positively-charged nucleus and negatively-charged electrons.

– Binding Energy eV~ 3000-8000 K

• Electron mass .5 MeV ~ 5x109 K

Atomic nuclei• The nucleus is itself made up of:

– Protons, p (positively charged)– Neutrons, n (neutral; no charge)– Collectively, these particles are known as

baryons– p is slightly less massive than n (0.1%

difference)– Protons and neutrons bound together by the

strong nuclear force (exchange of “gluons”)– Binding Energy per nucleon few Mev~1010 K

Elements & isotopes• Number of protons determines element:

– Hydrogen – 1 proton– Helium – 2 protons– Lithium – 3 protons– Beryllium – 4 protons– Boron – 5 protons– Carbon – 6 proton– …

• Number of neutrons determines the isotope• e.g., for hydrogen (1 proton), there are three isotopes

– Normal Hydrogen (H or p) – no neutrons– Deuterium (d) – 1 neutron– Tritium (t) – 2 neutrons

Quarks

• There’s one more level below this, consisting of quarks… – Protons & Neutrons are made up of trios of

quarks– Up quarks & Down quarks – Proton = 2 up quarks + 1 down quark– Neutron = 1 up quark + 2 down quarks– There are other kinds of quarks (strange,

charm, top, bottom quarks) that make up more exotic types of particles…

Quarks• In particle physics, quarks are one of the two basic constituents of matter (the other

Standard Model fermions are the leptons).• Antiparticles of quarks are called antiquarks. Quarks are the only

fundamental particles that interact through all four of the fundamental forces. The word was borrowed by Murray Gell-Mann from the book Finnegans Wake by James Joyce, where seabirds give "three quarks", akin to three cheers (probably onomatopoetically imitating a seabird call, like "quack" for ducks).

• The names of quark flavours (up, down, strange, charm, bottom, and top) were also chosen arbitrarily based on the need to name them something that could be easily remembered and used.

• An important property of quarks is called confinement, which states that individual quarks are not seen because they are always confined inside subatomic particles called hadrons (e.g., protons and neutrons); an exception is the top quark, which decays so quickly that it does not hadronize, and can therefore be observed more directly via its decay products. Confinement began as an experimental observation, and is expected to follow from the modern theory of strong interactions, called quantum chromodynamics (QCD). Although there is no mathematical derivation of confinement in QCD, it is easy to show using lattice gauge theory.

Nuclear fusion

• Heavier nuclei can be built up from lighter nuclei (or free n, p) by fusion

• Need conditions of very high temperature and density to overcome repulsion of protons

• These conditions are present only in cores of stars and… in the early Universe!

• The original motivation of Gamow, Alpher, & Herman in advocating big bang was that it could provide conditions conducive to nuclear reactions

The early universe must have been extremely hot and dense

Wien's displacement law

~

1 1~ ~

T const

R

TR

3 minutes

T about 109 K

History of Universe

according to BIG BANG

Theory

Planck Era

Before Planck time (~10-43 sec)

No theory of quantum gravity

Photons converted into particle-antiparticle pairs and vice-versa

E = mc2

Early universe was full of particles and radiation because of its high temperature

GUT Era

Lasts from Planck time (~10-43 sec) to end of GUT force (~10-38 sec)

Electroweak Era

Lasts from end of GUT force (~10-38 sec) to end of electroweak force (~10-10 sec)

Particle Era

Amounts of matter and antimatter nearly equal

(Roughly 1 extra proton for every 109 proton-antiproton pairs!)

Era of Nucleo-synthesis

Begins when matter annihilates remaining antimatter at ~ 0.001 sec

Nuclei begin to fuse

Era of Nuclei

Helium nuclei form at age ~ 3 minutes

Universe has become too cool to blast helium apart

Era of Atoms

Atoms form at age ~ 380,000 years

Background radiation released

Era of Galaxies

Galaxies form at age ~ 1 billion years

Primary Evidence

1) We have detected the leftover radiation from the Big Bang.

2) The Big Bang theory correctly predicts the abundance of helium and other light elements.

What have we learned?• What were conditions like in the early

universe?– The early universe was so hot and so dense

that radiation was constantly producing particle-antiparticle pairs and vice versa

• What is the history of the universe according to the Big Bang theory?– As the universe cooled, particle production

stopped, leaving matter instead of antimatter– Fusion turned remaining neutrons into helium– Radiation traveled freely after formation of

atoms

Evidence for the Big Bang

• How do we observe the radiation left over from the Big Bang?

• How do the abundances of elements support the Big Bang theory?

How do we observe the radiation left over from the Big

Bang?

The cosmic microwave background – the radiation left over from the Big Bang – was detected by Penzias & Wilson in 1965

Background radiation from Big Bang has been freely streaming across universe since atoms formed at temperature ~ 3,000 K: visible/IR

Expansion of universe has redshifted thermal radiation from that time to ~1000 times longer wavelength: microwaves

Background has perfect thermal radiation spectrum at temperature 2.73 K

WMAP gives us detailed baby pictures of structure in the universe

In early Universe…

• At t=1s, neutrinos began free-streaming• At t=14s, e stopped being created and destroyed• Temperature continued to drop until protons and neutrons, if

they combined, were not necessarily broken apart

NUCLEOSYNTHESIS IN THE EARLY UNIVERSE

• Nucleosynthesis: the production of different elements via nuclear reactions

• Consider universe at t=180s – i.e. 3 minutes after big bang– Universe has cooled down to 1 billion (109) K– Filled with

• Photons (i.e. parcels of electromagnetic radiation)• Protons (p)• Neutrons (n)• Electrons (e)• [also Neutrinos, but these were freely streaming]

The first three minutes…• Protons and Neutrons can fuse together to

form deuterium (d)

• But, deuterium is quite fragile…• Before t=180s, Universe is hotter than 1

billion degrees.– High-T means that photons carry a lot of energy– Deuterium is destroyed by energetic photons as

soon as it forms

n p D

D n p

After the first 3 minutes…• But, after t=180s, Universe has cooled to the

point where deuterium can survive• Deuterium formation is the first step in a

whole sequence of nuclear reactions:– e.g. Helium-4 (4He) formation:

DD T p

T D 4He n

Protons and neutrons combined to make long-lasting helium nuclei when universe was ~ 3 minutes old

Big Bang theory prediction: 75% H, 25% He (by mass)

Matches observations of nearly primordial gases

– Further reactions can give Lithium (Li)

– Reactions cannot easily proceed beyond Lithium due to the “stability gap”… more about that later

4He T 7Li

• If this were all there was to it, then the final mixture of hydrogen & helium would be determined by initial number of p and n.– If equal number of p and n, everything would basically

turn to 4He… Pairs of protons and pairs of neutrons would team up into stable Helium nuclei.

– Would have small traces of other species– But we know that most of the universe is hydrogen…

why are there fewer n than p? What else is going on?

Neutron decay

• Free neutrons (i.e., neutrons that are not bound to anything else) are unstable!– Neutrons spontaneously and randomly decay into

protons, emitting electron and neutrino

– Half life for this occurrence is 15 mins (i.e., take a bunch of free neutrons… half of them will have decayed after 15 mins).

epn

• While the nuclear reactions are proceeding, supply of “free” neutrons is decaying away.

• So, speed at which nuclear reactions occur is crucial to final mix of elements

• What factors determine the speed of nuclear reactions?– Density (affects chance of p/n hitting each other)– Temperature (affects how hard they hit)– Expansion rate of early universe (affects how quickly

everything is cooling off and spreading apart).

• Full calculations are complex. Need to:– Work through all relevant nuclear reactions– Take account of decreasing density and

decreasing temperature as Universe expands– Take account of neutron decay

• Feed this into a computer…– Turns out that relative elemental abundances

depend upon the quantity BH2

– Here, B is the density of the baryons (everything made of protons+neutrons) relative to the critical density.

B Bcrit

B

3H02 /(8G)

• Full calculations are complex. Need to:– Work through all relevant nuclear reactions– Take account of decreasing density and

decreasing temperature as Universe expands– Take account of neutron decay

• Feed this into a computer…– Turns out that relative elemental abundances

depend upon the quantity BH2

– Here, B is the density of the baryons (everything made of protons+neutrons) relative to the critical density.

B Bcrit

B

3H02 /(8G)

• We can use the spectra of stars and nebulae to measure abundances of elements– These need to be corrected for reactions in stars

• By measuring the abundance of H, D, 3He, 4He, and 7Li, we can– Test the consistency of the big bang model -- are

relative abundances all consistent?– Use the results to measure the quantity Bh2

How do the abundances of elements support the Big Bang

theory?

Bh2Mpcskm

Hh

//1000

From M.White’s webpage, UC Berkeley

Dependence of abundances on BH2

Bh2

Results

• All things considered, we have Bh20.019.

• If H0=72km/s/Mpc,– h=0.72 B0.04

• This is far below =1!• Baryons alone would give

open universe

What have we learned?

• How do we observe the radiation left over from the Big Bang?– Radiation left over from the Big Bang is

now in the form of microwaves—the cosmic microwave background—which we can observe with a radio telescope.

• How do the abundances of elements support the Big Bang theory?– Observations of helium and other light

elements agree with the predictions for fusion in the Big Bang theory

B 0.037

RECAP• The density parameter for matter is defined as

• Value of M very important for determining the geometry and dynamics (and ultimate fate) of the Universe

• Constraints from nucleosynthesis– To get observed mixture of light elements, we need the

baryon density parameter to be B0.037– If there were only baryonic matter (“normal” stuff made of

protons, neutrons, & electrons) in the Universe, then this would imply that M0.037.

– In that case, and if were =0, the Universe would be open (hyperbolic) and would expand forever

M mattercrit

matter

3H02 /(8G)

Standard model evolution diagrams

Preview…

• But life is more complicated than that…– Much evidence shows that M may be 5 or 10 times larger than

B , yet still M <1

– Additional evidence suggests that nevertheless, the Universe is flat, with k=0 so k =0 (i.e. neither hyperbolic nor spherical geometrically)

– This implies the cosmological constant must be nonzero…and in fact, there is observational evidence for accelerating expansion!

• We’ll start with the accounting of all forms of mass in the Universe…

THE MASS OF STARS IN THE UNIVERSE

• Stars are the easiest things to see and study in our Universe…– Can study nearby stars in detail– Can see the light from stars using “normal” optical

telescopes in even distant galaxies.

• But…what we see is the light, and what we’re interested in is the mass…

• Need to convert between the two using the mass-to-light ratio M/L.

The Sun

• Msun=21030 kg• Lsun=41026 W

• Actual numbers not very instructive…

• From now on, we will reference mass-to-light ratios to the Sun (Msun/Lsun).

Other stars

• Different types of stars have different mass-to-light ratios– Massive stars have small M/L (they shine

brightly compared with their mass).– Low-mass stars have large M/L (they are

very dim compared with their mass).– We’re interested in an average M/L

• Averaging regular stars near to the Sun, we get M/L3 Msun/Lsun

• But, we also need to include effect of “dead” stellar remnants… – white dwarfs, neutron stars, black holes.

• …and also sub-stellar mass objects– Called “brown dwarfs”– Interior gravity is too low to compress gas and initiate

fusion at very low luminosity

• All of these have mass M, but very little light L.– They add to the numerator of the average M/L, but not

to the denominator– Including the remnants and (smaller) brown dwarf

contribution, this would increase the mass-to-light ratio for spiral galaxies to about

M/L10 Msun/Lsun

• So, can add up the visible star light that we see in the Universe, and convert to a mass in stars (luminous and non-luminous).– We get L0.005-0.01– Comparing with B=0.037 from nucleosynthesis,

we see that most baryons cannot be in stars…

Where’s the rest of the baryonic matter if its not in stars?

• Galaxy clusters contain a lot of hot gas outside of individual galaxies– Gas temperature of 10-100

million K.

– Can see it using X-ray telescopes.

– Such gas contains a lot of the baryons

• The rest is believed to be in “warm/hot” (1 million K) gas in intergalactic space.

X-ray emission from the hot gas trapped in the Cygnus-A cluster

Real measurements

In outer parts of galaxies, V and R are based on measurements of hydrogen gas atoms orbiting galaxy, rather than stars

Called a dark matter “halo”

• Orbital velocity stays almost constant as far out as we can track it– Means that enclosed mass increases linearly with

distance – Mass continues to increase, even beyond the radius

where the starlight stops– While there is enough diffuse gas out there to track V,

it adds only a tiny amount of mass– So, in these outer regions of galaxies, the mass isn’t

luminous…– This is DARK MATTER.

• How big are galaxy halos?– We don’t know!– But they might be huge… maybe 10 times

bigger than luminous part of the galaxy!

• Add up all the galaxy halos… how much mass would there be? – Uncertain - we don’t know how far out

galaxy halos go.– Somewhere in range halos=0.1-0.3

Non-baryonic dark matter

• This is our first evidence for non-baryonic dark matter… B=0.04 (nucleosynthesis) halos=0.1-0.3 (galaxy rotation curves)

• So, there is substantially more mass in the galaxy halos than could possibly be due to baryons!

• Suggests a non-baryonic form of matter may exist… something not based on protons and neutrons.

MASS OF GALAXY CLUSTERS

• Galaxy clusters– Large groups of galaxies– Bound together by mutual gravitational

attraction– Let’s use same arguments for velocities

and radii of galaxies in cluster as for V and R of stars in galaxies (i.e., based on Newton’s laws) to measure mass…

Mcluster( R) Vgal2 R /G

The Virgo cluster

Dark matter in clusters • Find that here is a giant halo of

dark matter enveloping the galaxy cluster

• Includes the individual halos “attached” to each galaxy in cluster

• Also includes dark matter ripped from individual galaxies’ halos, or never attached to them

• Add up the mass in these cluster halos…

cluster=0.3• Some of this mass is in hot gas in

the cluster (contributing to B=0.04 from nucleosynthesis), but most is non-baryonic dark matter

Gravitational lensing…

• In some cases, can also measure cluster mass using gravitational lensing.

• Get good agreement with dynamical measurements

NON-BARYONIC DARK MATTER: SUMMARY

• Recap again…– Nucleosynthesis arguments constrain the density of

baryons (B0.037)– But there seems to be much more mass in galaxy and

cluster halos (total Matter=0.3)– So, most of the matter in the Universe is not baryonic!

• what is it????

The cosmic concordance

• What is our universe like?– Matter content?– Geometry (flat, spherical, hyperbolic)?– Anything else strange?

• Remarkable agreement between different experimental techniques:

“Cosmic concordance” parameters

Measurements of the matter content of the Universe (recap)

• Primordial nucleosynthesis– Theory predicts how present light element

abundances (4He, 3He, D, 7Li) depend on mean baryon density

– Observed abundances B0.04

• Galaxy/galaxy-cluster dynamics– Look at motions of stars in galaxies, or galaxies in

galaxy clusters…– Infer presence of large quantities of “dark matter”

which gravitationally affects observed objects but cannot be seen with any telescope

• Analysis of galaxy motions suggests a total matter density of Matter0.3

• Same conclusion from gravitational lensing by clusters (light from background objects is bent due to GR effects)

• First stunning conclusion:– Compare B0.04 and Matter0.3

– Normal matter only accounts for about 1/8 of the total matter that’s out there!

– Dark matter provides DM0.26

– We’re made of the minority stuff!

• Can be confirmed by taking an inventory of a cluster, where diffuse gas is hot and emits X-rays…– Find that about 1/8 of a

cluster’s mass is in baryons– We believe that clusters

should be representative samples of the universe…

– Confirms DM0.26

MEASURING THE GEOMETRY OF THE UNIVERSE

• Recall that universe with different curvature has different geometric properties

• Adding up the angles in a triangle,– Flat universe(k=0): angles sum to 180– Spherical universe (k=+1): angles sum to >180– Hyperbolic universe (k=-1): angles sum to <180

• Similarly, for a known length L at a given distance D, the angular size on the sky varies depending on the curvature of space– Flat universe (k=0): angular size =L/D– Spherical universe (k=+1): angular size >L/D– Hyperbolic universe (k=-1): angular size <L/D

D

L

k=0 k=+1 k=-1

L L

Angular size of fluctuations in the CBR

• Remember the cosmic microwave background…

• It has fluctuations, with average separations corresponding to a known scale L at the distance where light last interacted with matter (matter/radiation decoupling)

• Distance D to this “surface of last scattering” is also known

• Can use apparent angular separations of fluctuations compared to L/D to infer geometry of Universe

us

D L

Flat universe!• Result:

– The universe is flat– In terms of omega curvature parameter,

k=0, i.e k=0– Recall that the sum of all three omega parameters as

measured at present time must be 1:

– How do we reconcile k=0 with our measurement of the matter density, which indicates M=0.3?

– There must be a nonzero cosmological constant, =0.7!

1M k

M 0

crit

0

(3H02 /8G)

k kc 2

R02H0

2

3H02