How to evade the CMB limit on Dark Matter interactions

One of the probes used to constrain Dark Matter (DM) is the Cosmic Microwave Background (CMB) bound, deriving from the small modifications on the CMB spectrum due to the interactions between photons and the free particles produced by DM annihilation. After a general introduction to Dark Matter physics and the CMB, in this thesis we will analyze different scalar and fermionic operators entering the interactions between Dark Matter and Standard Model particles to determine whether the thermally-averaged cross-section <σv> is s- or p-wave. In particular, we will try to bypass the computation of the total amplitude of the process, focusing directly on the structure of the DM fermionic bilinear in the non-relativistic limit. This study is aimed at determining which DM candidates evade the CMB bound by construction. Indeed, unlike s-wave annihilation processes, where <σv> is velocity-independent and can be probed by the CMB bound, p-wave annihilation processes evade it since, in that case, <σv> is proportional to v^2, so it is strongly suppressed by the time of recombination.