Spectral Distortions of the Cosmic Microwave Background

Studying the cosmic microwave background (CMB) has proven to be an
immensely rich source of information about the Universe we live in.
Many groups were and are intensely working on the interpretation of
the large amount of CMB data, which has become available during the
last decades and will be obtained with many new projects already
observing at present or planned for the near future. The
observations by COBE in the 90's have shown that the CMB is
extremely uniform, with angular fluctuations of the temperature on
the level of one part in 10^5 on angular scales larger than 7
degree. On the other hand on these scales no deviations of the CMB
energy spectrum from a perfect blackbody were found. But today we
do know that there exist spectral distortions of the CMB on
arcminute scales due to the scattering of CMB photons off the hot
electrons residing inside the deep potential well of clusters of
galaxies, which leads to the so called thermal-SZ effect (th-SZ).
The th-SZ effect has already been measured for several big cluster
and within the next 5 years, many CMB experiments like ACBAR, SZA,
PLANCK, SPT, ACT, APEX, AMI and QUIET will perform deep searches
for clusters with very high sensitivity. Many tens of thousands of
clusters will be detected allowing us to carry out detailed studies
of cluster physics and to place constraints on parameters of the
Universe. Due to this great advance in technology one can expect
that small deviations from the main SZ cluster signal, e.g. related
to relativistic corrections to Compton scattering for high electron
temperature, will become observable. Motivated by this promising
perspective here we studied the influence of the motion of the
Solar System with respect to the CMB rest frame on the SZ cluster
signature. This kind of contribution to the SZ signal has been
neglected in the literature so far, but as we show here it is of
the same order as other corrections under discussion. We found that
this motion-induced SZ signal has a very strong spectral and
spatial dependence and due to the great knowledge about the
motion-induced CMB dipole it can be predicted with high precision,
which makes it easy to account for it in the analysis of future SZ
studies. Here one big problem naturally arises: any experiment
trying to observe tiny frequency-dependent signals needs a cross
calibration of the different frequency channels. Several different
standard methods for calibration issues are known, e.g. based on
the annual modulation of the CMB dipole, the microwave flux from
planets like Jupiter or the comparison with CMB sky maps obtained
by well calibrated experiments like WMAP, each with their own
problems and drawbacks. However the achieved level of cross
calibration is limited by the knowledge of the calibrator. Today
scientists are already speaking about extremely small
frequency-dependent features in the CMB temperature power spectrum
resulting from the scattering of CMB photons in the fine structure
lines of different atomic species during the dark ages. Obtaining
these signals can in principle be used to answer some of the
interesting questions about the history of chemical enrichment and
reionization, but it is likely that the necessary level of cross
calibration cannot be reached with the standard methods. In this
context we considered the fact that the superposition of
blackbodies with different temperatures is not again a blackbody.
We show that in the limit of small temperature difference the
superposition leads to a y-type spectral distortion. This kind of
distortion arises whenever one in observing the CMB sky with finite
angular resolution. We discuss the spectral distortions due to the
primordial CMB temperature fluctuations and the motion-induced CMB
dipole. Furthermore we considered possible applications for
calibration issues. We show that within this context also clusters
of galaxies, especially for experiments observing only small parts
of the sky, in the future may become standard sources for
calibration issues. Although the observations with COBE/FIRAS have
proven that the CMB energy spectrum on large angular scales is
extremely close to a pure blackbody one may still expect some
deviations due to processes like the damping of acoustic waves,
turbulent motion of the matter, the decay of unstable particles or
annihilation of matter in the early Universe. Especially possible
distortions from very early epochs (redshifts z> few x 10^5)
lead to deviations of the CMB brightness temperature at frequencies
(1-few x 10 GHz) well below the range of COBE/FIRAS. Currently
people in the USA and especially at the NASA Goddard Space Flight
Center are intensely working on experiments to measure the CMB
temperature at these frequencies, where the largest distortions
could be expected. One can therefore hope that in the near future
also new constraints on the CMB energy spectrum will become
available. Therefore in this thesis we also reexamined the
thermalization of spectral distortions of the CMB in the early
Universe. Due to the large entropy here one of the most important
processes is the production of low frequency photons by double
Compton scattering. Until now people were only using a description
of this emission in the limit of cold electrons and soft initial
photons, but especially for the thermalization of large distortions
at very high redshifts (z > 10^6) the inclusion of relativistic
corrections to the main processes at work may become necessary.
Here we provide two steps towards a solution of this problem. First
we discuss in detail the full kinetic equation for the time
evolution of the photon field under double Compton scattering in a
hot, isotropic thermal plasma, both numerically and analytically.
We obtained accurate approximations for the effective double
Compton Gaunt factor, which are applicable in a very broad range of
physical situations. We then provide a reformulation of the
thermalization problem with respect to relativistic corrections and
discuss its solution in the limit of small chemical potential
distortions at high redshifts. Our results indicate that due to
relativistic corrections the thermalization at high redshifts slows
down notably and therefore makes the CMB more vulnerable for
distortions at epochs z > 10^6. Here we also report some of our
attempts to solve the full problem numerically.