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 CMB
Photons 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.
free charged particles,
strong photon scattering
neutral hydrogen atoms,
no photon scattering
last scattering
time
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?
ANISOTROPIES!!!!!!!
ignore this, it’s just Milky Way
COBE map of CMB
The big dipole
Our galaxy is moving with respect to CMB and we see parts
of it shifted due to Doppler effect.
Correlation functions
Correlation functions give us information on the structures
existing in the spectrum of our data or given mathematical
function
Two point correlation function of f(x):
C     f x    f x dx
A simple example – the data
Data
1
0,8
0,6
0,4
0,2
n
-0,4
-0,6
Measurement number n
70
65
60
55
50
45
40
35
30
25
20
15
10
-0,2
5
0
0
Signal amplitude f(n)
f(n)
A simple example – the
correlation
C(k)
14
12
Two point correlation function
12,1
10
8
6,6
6,5
6
4
2,1
2
3,1
3
2,7 2,5 2,4
2,4 1,8
1,7
0
0
1
2
Correlation:
3
4
5
6
7
8
9
10
C k    f n  k  f n 
n
11
k
A simple example – the truth
The data:
U (0.5,0.5)  0.6 for n divisible by 4
f n   
U (0.5,0.5)  0.0 for n not divisible by 4
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): C   
Anisotropies of CMB angular spectrum:

n
 f x    f x dx
T 
T
n .
vector is a pair of angular coordinates  and .
Two point correlation function of CMB:
T  T 
T
n 
T
n '

nn 'cos
2l+1 dipole
moments
2l  1

Cl Pl cos  
4
l
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
C     f x    f x dx
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
massive spring (high baryon density)
light spring (low baryon density)
The higher baryon density, the more
compressed the fluid. And it shows in
the peaks!
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.
Y
X
Quadrupole anisotropies
‘Darkness [...] was the Universe’
Lord Byron, Darkness
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
Precision cosmology
Total energy density (BOOMERanG data)  is
estimated to be 1.020.06. (=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 0.720.08 *
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