Cosmic Microwave Background (CMB)

Peter Holrick

and

Roman Werpachowski

Beginnings of the Universe

Big Bang inflation period further expansion and

cooling of the universe particle creation and

annihilation equilibrium between matter

and radiation; first dominated by radiation, then by matter

light had a perfect black body spectrum

Photon-baryon fluid

Last scattering

Some 300,000 yrs after the Big Bang, the temperature was low enough (~3000 K) to allow electrons to combine with protons, making hydrogen atoms.

Intensive Thomson scattering on charged particles in photon-baryon plasma IS OUT

Low-effective Rayleigh scattering or absorption of a discrete spectrum of frequencies by neutral hydrogen atoms (or particles) COMES IN

Universe becomes transparent to light.

Origins of CMBPhotons released in the ‘last scattering’ form CMB as

it is measured today.History of the Universe up till this point in time shows

in CMB.

last scattering

free charged particles,strong photon scattering

time

neutral hydrogen atoms, no photon scattering

What happened to CMB next? CMB temperature is

inversely proportional to the R scale factor (radiation density is proportional to the R-4 and any fixed volume expands as R3). R was equal to 0 in the Big Bang and equals 1 „now”.

Since the last scattering, CMB temp. fell because of space expansion from ~3000 K to 2.728 K now. However, it retained a perfect black body spectrum.

What do we see in CMB?

ignore this, it’s just Milky Way COBE map of CMB

ANISOTROPIES!!!!!!!ANISOTROPIES!!!!!!!

The big dipole

Our galaxy is moving with respect to CMB and we see partsof it shifted due to Doppler effect.

Correlation functions

Two point correlation function of f(x):

dxxfxfC

Correlation functions give us information on the structures existing in the spectrum of our data or given mathematical function

A simple example – the data

Data

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0,8

1

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Measurement number n

Sig

nal a

mpl

itud

e f(

n)

n

f(n)

A simple example – the correlation

Two point correlation function

12,1

2,13,1 3

6,6

2,7 2,5 2,4

6,5

2,4 1,8 1,7

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 10 11

n

nfknfkCCorrelation:

C(k)

k

A simple example – the truth

4by divisiblenot n for 0.0 )5.0,5.0(

4by divisiblen for 6.0)5.0,5.0(

U

Unf

The data:

Where U(-0.5,0.5) is a random number with a uniform distribution between –0.5 and 0.5

Correlations in CMB

Two point correlation function of f(x): dxxfxfC

Two point correlation function of CMB:

Anisotropies of CMB angular spectrum: .nT

T

n

vector is a pair of angular coordinates and .

lll

nn

PCl

nT

Tn

T

T

cos

4

12'

cos'

2l+1 dipole moments

Integrating on a sphere

Structures young and old

Gravitational attraction

(film by Andrey Kravtsov)

Photon-baryon oscillations

Proof of gravitational potential fluctuations in the early Universe.

Peaks in CMB spectrum

Peaks in CMB spectrum

dxxfxfC

Curvature and angle of vision

Peaks and curvature

Remember, we’re talking about the curvature of a 3D space!

Negative curvature (open Universe) shifts the whole CMB spectrum to higher l’s (lower angles).

Baryon loading

The higher baryon density, the morecompressed the fluid. And it shows in the peaks!

light spring (low baryon density)

massive spring (high baryon density)

Photon-baryon oscillations

Proof of gravitational potential fluctuations in the early Universe.

Peaks in CMB spectrum

Damping

There is a substantial suppression of peaks beyond the third one, due to acoustic oscillation damping.

Damping can be thought of as a result of a random walk in the baryons that takes photons from cold to hot regions and vice versa, smoothing out small-scale temperature inhomogeneities.

This random walk is due to the mean free path of a photon in the photon-baryon fluid – photons slip through the baryons for short distances.

Radiation driving Radiation decayed potential wells in the radiation era. This alone would enhance high l oscillations and

eliminate alternating peak heights from baryon loading. This effect depends strongly on the cold dark matter

(CDM) to radiation ratio.

Polarization Very small,

generated only by scattering at recombination.

Caused by quadrupole anisotropies.

Can be caused by gravitational waves or vortices.

XY

Quadrupole anisotropies

‘Darkness [...] was the Universe’

First peak tells that the Universe is flat.

Second peak tells that density of baryon matter b is too low for a flat Universe.

High third peak tells that radiation could not eliminate baryon loading.

Damping of higher l peaks tells that photons could slip through baryon matter and dissipate across potential fluctuations.

there is cold dark matter and dark energy in the Universe

Lord Byron, Darkness

Precision cosmology Total energy density (BOOMERanG data) is

estimated to be 1.020.06. (=1 means flat Universe). Baryon density is estimated1 to be bh2 = 0.02.

Consistent with other estimations (deuterium in quasar lines and the theory of big-bang nucleosynthesis).

Dark energy density is estimated to be between 0.5 and 0.7 (data from galaxy clustering and type Ia supernovae luminance).

Dark matter is constrained by CMB to dmh2=0.13 0.04.

1Hubble constant h is taken to be 0.720.08 * 100km/s/MPc (data from HST).

Summary Due to low density of matter, light from the Universe

300,000 years old (age of recombination) reached us almost unchanged.

It is much colder due to expansion of the Universe. It has Gaussian fluctuations which can be completely

described by their power spectrum. We see peaks in the power spectrum. Those peaks are due to oscillations of light and matter

before the recombination. Those peaks are an immensely fruitful source of

information for the cosmologists. We are going to measure them more precisely than now!

Sources

http://background.uchicago.edu

What’s Behind Acoustic Peaks in the Cosmic Microwave Background Anisotropies, arXiv:astro-ph/0112149

CMB and Cosmological Parameters: Current Status and Prospects, arXiv:astro-ph/0204017

Bernard F. Schutz, A First Course in General Relativity