Langevin simulation of dark matter kinetic equilibration

Recently it has been questioned, notably in the context of the scalar singlet dark matter model with $m_\varphi^{ }\simeq 60$ GeV, how efficiently kinetic equilibrium is maintained if freeze-out dynamics is pushed down to low temperatures by resonant effects. We outline how Langevin simulations can be employed for addressing the non-equilibrium momentum distribution of non-relativistic particles in a cosmological background. For a scalar singlet mass $m_\varphi^{ }\simeq 60$ GeV, these simulations suggest that kinetic equilibrium is a good approximation down to $T \sim 1$ GeV, with the deviation first manifesting itself as a red-tilted spectrum. This reduces the annihilation cross section, confirming findings from other methods that a somewhat larger ($ < 20\%$) coupling than in equilibrium is needed for obtaining the correct abundance.