Cosmic Microwave Background (CMB)
Peter Holrickand
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
Sign
al a
mpl
itude
f(n)
n
f(n)
A simple example – the correlation
Two point correlation function12,1
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(
UU
nf
The data:
Where U(-0.5,0.5) is a random number with a uniform distribution between –0.5 and 0.5
Correlations in CMBTwo point correlation function of f(x): dxxfxfC
Two point correlation function of CMB:
Anisotropies of CMB angular spectrum: .nTT
n vector is a pair of angular coordinates and .
lll
nn
PClnTTn
TT
cos
412'
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