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. 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 R 3 ). 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 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!!!!!!!

The big dipole Our galaxy is moving with respect to CMB and we see parts of it shifted due to Doppler effect.

Correlation functions Two point correlation function of f(x): Correlation functions give us information on the structures existing in the spectrum of our data or given mathematical function

A simple example – the data Measurement number n Signal amplitude f(n) n f(n)

A simple example – the correlation Correlation: C(k) k

A simple example – the truth 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): Two point correlation function of CMB: Anisotropies of CMB angular spectrum: vector is a pair of angular coordinates  and . 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

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 more compressed 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. X Y

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 1.02  (  =1 means flat Universe). Baryon density is estimated 1 to be  b h 2 = 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  dm h 2 =0.13  Hubble 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 What’s Behind Acoustic Peaks in the Cosmic Microwave Background Anisotropies, arXiv:astro-ph/ CMB and Cosmological Parameters: Current Status and Prospects, arXiv:astro-ph/ Bernard F. Schutz, A First Course in General Relativity