The Frequency Spectrum of the CMB

This final chapter discusses spectral distortions of the CMB. We first introduce the relevant collision processes in a universe with photons and non-relativistic electrons: Compton scattering, Bremsstrahlung and double Compton scattering. We derive the corresponding collision terms and Boltzmann equations. For Compton scattering this leads us to the Kompaneets equation for which we present a detailed derivation. We introduce timescales corresponding to these three collision processes and determine at which redshift a given process freezes, i.e., becomes slower than cosmic expansion. We also discuss the generation of a chemical potential in the CMB spectrum by a hypothetical particle decay and by Silk damping of small scale fluctuations. Finally, we study the Sunyaev{Zel’dovich effect of CMB photons which pass through hot cluster gas.