xi. the hot big bang and the cosmic microwave...

XI. The Hot Big Bang and the Cosmic Microwave Background

ASTR378 Cosmology : XI. Hot Big Bang and CMB 143

Properties of the CMB

•  The Cosmic Microwave Background (CMB) has the spectrum of a blackbody with T0 = 2.725±0.001 K

•  Energy density of radiation:


�

εγ ≡ ρradc2 = αT 4

α = π 2kB4

15h3c 3≈7.565×10-16 J m-3 K-4

Critical Density and the CMB

•  At the present day, the energy density in the CMB is

which, as a fraction of

ρcrit gives Ωγ(t0)~ 5×10-5, << than Ωbary(t0)~0.04

•  We know the radiation density goes as

so the Universe cools as it expands

•  The spectrum of the CMB is still a blackbody, just at a lower temperature

•  ρrad(t0) << ρbary(t0) ; what about the numbers of photons and baryons?


�

εγ ≡ ρradc2 = αT 4 ≈ 4.2 × 10-14 J m-3,

�

ρrad ∝1a4; ρrad ∝T

4

�

T ∝ 1a

The Photon / Baryon Ratio

•  If we divide the energy density of the CMB by the mean energy per photon, we get nγ(t0) ~ 4.11 × 108 m-3

•  We can get the number density of baryons from Ωbary ~ 0.04 and the mass of a proton (≈ mass of a neutron) nbary(t0) ~0.22 m-3

•  The ratio of baryons to photons η≈ 5 × 10-10 there are roughly two billion photons for every baryon (!)



Recap: The Origin of the CMB

•  Early Universe much hotter and denser typical γenergetic enough to ionise H a “sea” of nuclei and e-

•  γinteract strongly with free e- frequent collisions, short mean free path of γ Universe opaque

•  As the Universe expanded and cooled, <εγ> , typical γ no longer able to ionise H γ can travel freely decoupling


Recap: The Surface of Last Scattering

•  Decoupling occurred when the Universe was ~ 3000 K, before then in a highly-interacting thermal state uniform (to ~10-5) BB spectrum in all directions (steady state theory)

•  CMB photons come from when the Universe was ~1100× smaller, and originate from a sphere surface of last scattering (more like a layer...)

Schematic View of the History of the Universe ASTR378 Cosmology : XI. Hot Big Bang and CMB 149

CMB Temperature Fluctuations

•  COBE spacecraft (1990’s): –  to 1st order, the CMB is uniform –  the CMB dipole, resulting from motion of

the satellite relative to the CMB (Earth – Sun, Sun – Galaxy, etc.)

–  Once you subtract out the dipole and foreground emission from the Milky Way, you get:


�

T = 14π

T θ,φ( )∫ sinθ dθ dφ = 2.725Κ

δTT

θ,φ( ) ≡ T θ,φ( ) − TT

; δTT

⎛ ⎝ ⎜

⎞ ⎠ ⎟ 2 1/ 2

≈1.1×10−5

COBE and WMAP


COBE (1990’s) WMAP (2000’s)

The Scale of CMB Temperature Fluctuations

•  Can express δT/T in terms of spherical harmonics:

•  Correlation function of δT/T:

•  Cl measures temperature fluctuations on an angular scale θ~180°/l (l = 0: monopole, l = 1: dipole, l ≥ 2: cosmologically interesting)


�

δTT

θ,φ( ) = almYlm θ,φ( )m=− l

l

∑l= 0

∞

∑

�

C θ( ) = 14π

(2l +1)Cll= 0

∞

∑ Pl cosθ( )

The Causes of CMB Temperature Fluctuations

•  Different origins for large-scale (l < 180) and small-scale (l> 180) fluctuations

•  Large-scale fluctuations: inhomogeneities in dark matter distribution affect energy of photons Sachs-Wolfe effect

•  Small-scale fluctuations: acoustic oscillations of photon-baryon fluid, peak in ΔT depends on curvature


ΛCDM Cosmology

•  Current observational constraints on Ωmat and ΩΛ from three different sources: –  Type Ia supernovae (SNe, blue) –  Sound waves in the Cosmic Microwave

Background (CMB, orange) –  Large-scale structure in the distribution of

galaxies (Baryon Acoustic Oscillations=BAO, green)

•  They all overlap at the same location •  They all overlap where Ωmat + ΩΛ≈ 1;

best guess Ωmat ~ 0.3, ΩΛ~ 0.7


From Kowalski et al. 2008

Contours:68.3%, 95.4% and 99.7% confidence levels

k > 0

k < 0

xi. the hot big bang and the cosmic microwave...

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