Momentum distributions of cosmic relics: Improved analysis
  We present a framework for solving a coupled set of momentum-dependent
Boltzmann equations for the phase space distribution of cosmic relic particles,
without resorting to approximations of assuming kinetic equilibrium or
neglecting back scattering or elastic interactions. Our framework is amendable
to precision numerical computations. To test it, we consider two benchmark
models where the momentum-dependence of dark matter distribution function is
potentially important: a real singlet scalar extension near the Higgs
resonance, and a sterile neutrino dark matter model with a singlet scalar
mediator. The singlet scalar example shows that even near sharp resonances the
kinetic equilibrium holds well enough to justify the use of integrated
momentum-independent Boltzmann equation in preliminary parameter scans.
However, the integrated method may underestimate the relic density by up to 40%
in extreme cases. In the sterile neutrino dark matter model we studied how the
inclusion of previously ignored elastic interactions and processes with initial
state sterile neutrinos could affect the non-thermal nature of their resulting
distributions. Here the effects turned out to be negligible, proving the
robustness of the earlier predictions.
