Thermal decoupling of WIMPs from first principles

Weakly interacting massive particles (WIMPs) are arguably the most natural DM candidates from a particle physics point of view. After their number density has frozen out in the early universe, determining their relic density today, WIMPs are still kept very close to thermal equilibrium by scattering events with standard model particles. The complete decoupling from the thermal bath happens as late as around $\sim1-10 $MeV, thereby setting an important cosmological scale that can directly be translated into a small-scale cutoff of the spectrum of matter density fluctuations. We present here a full analytic treatment of the kinetic decoupling process from first principles. This allows an exact determination of the decoupling scale, for an arbitrary WIMP candidate and any scattering amplitude. As an application, we consider the situation of the lightest supersymmetric particle as well as the lightest Kaluza-Klein particle that arises in theories with universal extra dimensions; furthermore, we show that our formalism can also easily be applied to, e.g., the evolution of the non-relativistic electrons into the recombination regime. Finally, we comment on the impacts for the smallest gravitationally bound structures and the prospects for the indirect detection of dark matter