A Bit of History• 1917: William de Sitter uses general relativity to describe an

expanding universe• 1917: Einstein, preferring a static, unchanging universe, adds

a constant of integration, the �Cosmological Constant�• 1929: Hubble discovers that the universe is expanding!!

Hubble’s original redshift-distance diagram

A Bit of History• 1917: William de Sitter uses general relativity to describe an

expanding universe• 1917: Einstein, preferring a static, unchanging universe, adds

a constant of integration, the �Cosmological Constant�• 1929: Hubble discovers that the universe is expanding!!• 1927: George Lemaître makes the first estimate of the

“Hubble Constant,’’ and proposes the Big Bang model of theuniverse. (Note: the term “Big Bang” wasn’t coined untilmuch later, when Fred Hoyle was trying to discredit it.)

• 1948: George Gamow predicts the existence of backgroundradiation from the Big Bang using nucleosynthesis arguments

Gamow’s Argument• In its first second, the universe must have been a hot, dense

mixture of electrons, protons, neutrons, neutrinos, and photons• At an age of ~ 1 sec, the ratio of protons to neutrons must have

been unity as interactions with neutrinos mediate theconversion of neutron to protons, and vice versa

• At an age of ~2 sec, the universe would have expandedenough to allow neutrinos to escape. This would have causethe ratio of protons to neutrons to increase.

• Later, when the universe cooled enough for fusion to occur,the proton-neutron ratio would have been ~7. Nucleosynthesis(the proton-proton chain) would have made the mass fractionof helium ~ 0.25. This is what is observed.

• Thus the universe must have been very hot at one point,leading to a background radiation.

A Bit of History• 1917: William de Sitter uses general relativity to describe an

expanding universe• 1917: Einstein, preferring a static, unchanging universe, adds

a constant of integration, the �Cosmological Constant�• 1929: Hubble discovers that the universe is expanding!!• 1927: George Lemaître makes the first estimate of the

“Hubble Constant,’’ and proposes the Big Bang model of theuniverse. (Note: the term “Big Bang” wasn’t coined untilmuch later, when Fred Hoyle was trying to discredit it.)

• 1948: George Gamow predicts the existence of backgroundradiation from the Big Bang using nucleosynthesis arguments

• 1965: Arno Penzias and Robert Wilson discover the noise ina radio antennae won’t go away. It is the 2.73 K cosmicmicrowave background radiation (CMB).

Penzias and Wilson and their microwave antenna

The Cosmic Microwave BackgroundIf the universe is expanding, then at one time, it must have been verydense, and (through the equation of state) very hot. It thereforeemitted blackbody radiation. When the universe is ionized, photonsinteracted with matter, and their mean-free path was short; oncerecombination occurred, interactions ceased and the universe becametransparent. These photons are still with us today, though they havebeen redshifted.

Temperature versus Time Density versus Time

Tem

pera

ture

[Kel

vin]

Log

Den

sity

Time [Gyr] Time [Gyr]

17,000 years old100,000 Kelvin

17,000 years old10 trillion atoms per m3

13 billion years old0.1 atoms per m313 billion years old

3 Kelvin

Temperature Evolution of the Microwave Background

The expansion of the universe has caused the matter density of theuniverse to drop by (1+z)3, the photon energy to decline as (1+z), andthe microwave background temperature to decline as (1+z).

The Cosmic Microwave BackgroundWe can calculate the epoch of last scattering through the Sahaequation. Recall that

€

Ni+1

Ni

Ne = 2 2πmekTh2

#

$ %

&

' ( 3 / 2 ui+1

uie−χ / kT

For pure hydrogen, Ne = Ni+1, N = Ni + Ni+1, ui+1= 1, and ui= 2. If welet x = Ni+1/N, and substitute ρ = N mH, T = T0 (1+z), and ρ = ρ0(1+z)3, then

The universe became transparent when it went from being ionized toneutral, i.e., when x ~ 0.5. Through the equation, this corresponds toz ~ 1500, and a recombination temperature of T ~ 4000 K.

x2

1− x=2πmekT0

h2⎛

⎝⎜

⎞

⎠⎟3/2 mH

ρ01+ z( )−3/2 e−χ /kT0 (1+z)

The Cosmic Microwave Background• 1948: 3 degree blackbody emission from the entire universe

predicted by George Gamow• 1965: 3 degree blackbody emission found by Arno Penzias and

Robert Wilson• 1998: Blackbody spectrum measured by the COBE satellite

Note the size of the error bars!!!

Initial Perturbation

Consider a uniform uni-verse with cold (slow-moving) dark matter,baryonic gas, photons,and hot (fast-moving)neutrinos. Now add in asmall positive densityperturbation that affectsall species.

Since the gas is ionized,photons have very smallmean-free paths, and arestrongly coupled to thegas.

The Uniformity of the CMB

Acoustic Wave Begins to Propagate

Since the dark matter iscold and (at very best)weakly interacting, itstays put, gravita-tionally attracting other(dark) matter.

Since neutrinos are hotand non-interacting,they stream out freely.

The over-density of gasand photons causes apressure wave topropagate.

The Uniformity of the CMB

Matter infalling to the dark matter clump

Photons and neutrinosleave the centralperturbation, leaving aconcentration of darkmatter. The neutrinoscontinue to spread out,and the acoustic wave(driven largely by theenergy of the photons)continues to propagate.

The Uniformity of the CMB

The beginning of decoupling.

The universe cools, sothe gas begins torecombine. Photonsbegin to leak throughthe partially neutralgas, decreasing thespeed of the pressurewave until it stalls.After recombination,photons are free tostream across theuniverse.

The Uniformity of the CMB

The Acoustic Wave

Structure begins to grow

The dark matter andgas perturbations bothbegin to attract mattergravitationally. Bothperturbations increasein strength and start togrow by many ordersof magnitude.

The Uniformity of the CMB

Dark matter begins accumulate in theacoustic peak, and gas falls into the darkmatter peak.

The photons andneutrinos are nowdistributed (almost)uniformly across theuniverse. The pertur-bations continue togrow in amplitude asmatter falls into thepotential wells. Thus,the distributions of gasand dark matter beginto look the same.

The Uniformity of the CMB

The potential wells defined by the darkmatter begin to define the distribution of allmatter.

The acoustic peak’scontrast begins todecline, as the gas isforced to follow thepotential defined bythe (five times moremassive) dark mattercomponent.

The Uniformity of the CMB

The distribution of galaxies at later times.

Galaxies now form inthe regions of highestdensity. A ~ 1%enhancement in thegalaxy density existsroughly 150 Mpc fromthe primary peak.

The Uniformity of the CMB

The Dominance of Dark Matter

Note: most of the structurewe see in today’s universecomes simply from thegravitational attraction ofcollisionless dark matter.The baryons are largely justaround for the ride.

The Dominance of Dark Matter

Note: most of the structurewe see in today�s universecomes simply from thegravitational attraction ofcollisionless dark matter.The baryons are largely justaround for the ride.

The Microwave Background FluctuationsAll the individual fluctuations overlap, but the acoustic peak is stillimprinted in the universe.

The All-Sky Microwave BackgroundBecause the Earth is moving through space, the microwavebackground has a dipole moment. COBE observed this quite easily.

The direction of the Earth’s motion is towards α(2000) = 11h 09m, δ(2000) = -6� 42�

The All-Sky Microwave BackgroundWhen the Earth’s motion is removed, the distribution of microwaveson the sky becomes more uniform.

The plane of the Milky Way is easily visible. This is due to thermalemission from cold dust and synchrotron emission from high energyelectrons (produced by supernovae, etc.)

The All-Sky Microwave Background

The fluctuations are only a few parts in 10,000

Finally, after removing the Milky Way’s emission, we are left with theprimordial fluctuations in the microwave background.

The All-Sky Microwave BackgroundThe spatial resolution of WMAP was much greater than that ofCOBE, allowing better measurements of δT/T versus position.

Simplified Power Spectra

The fluctuations in themicrowavebackground can bequantified by turningthe observed spatialdistribution of hot andcold regions into apower spectrum.

Cosmic Microwave Power Spectrum

The temperature fluctuations, DT, are translated into the coefficientsof spherical harmonics (note q = 2p/l)

The power spectrum is then the sum of the squares of the coefficients

(with the normalization)

€

ΔT(θ,φ) = al ,m∑ Yl,m (θ,φ)

€

Cl =1

2l +1al ,m2

m∑

€

ΔT2 =

l l +1( )2π

ClT2

Cosmological ParametersThe amplitude and location of the acoustic peak depends oncombination of• The expansion rate of the universe• The fraction of cold dark matter in the universe• The fraction of baryons in the universe• The fraction of hot neutrinos in the universe• The epoch when the energy and matter densities were equal• The amplitude of the initial fluctuations

The amplitude and location of where we observe the acousticpeak to be depends on• The curvature of the universe• The amount of dark energy in the universe• The epoch of re-ionization

Geometry MeasurementsOur measurement of the angular position of the acoustic peakdepends on the shape of the universe.

The Observed CMB Power Spectrum

The Observed CMB Power Spectrum

The Observed CMB Power Spectrum

Angular power spectrum, courtesy of Wayne Hu

Parameter Dependence of Power spectrum -- Hu & Dodelson (2002)

Cosmic Microwave BackgroundWMAP and Planck have strongly confirmed the LCDM modelimplied by the Type Ia supernovae results!! Presently, the best-fitparameters (assuming a Cosmological Constant with k = 0) are:• WL= 0.6911 � 0.0062• H0 = 67.74 � 0.46 km/s/Mpc • Wmatter= 0.3089 � 0.0062• Wbaryon = 0.0486 � 0.0010• Ωdark = 0.2589 � 0.0057• Wn < 0.003 (95% CL) • Age of the universe is 13.799 � 0.021 Gyr

If the requirement of flatness is released, then• Wtot= 1.0023 � 0.0055• w = -0.98 � 0.053

The best constraints oncosmological parameters comefrom a combination of data,including supernovae, theCMB, the large scale structureof galaxies, and the growth ofgalaxy clusters.