Early kinetic decoupling of dark matter: when the standard way of
  calculating the thermal relic density fails
  Calculating the abundance of thermally produced dark matter particles has
become a standard procedure, with sophisticated methods guaranteeing a
precision that matches the percent-level accuracy in the observational
determination of the dark matter density. Here, we point out that one of the
main assumptions in the commonly adopted formalism, namely local thermal
equilibrium during the freeze-out of annihilating dark matter particles, does
not have to be satisfied in general. We present two methods for how to deal
with such situations, in which the kinetic decoupling of dark matter happens so
early that it interferes with the chemical decoupling process: i) an
approximate treatment in terms of a coupled system of differential equations
for the leading momentum moments of the dark matter distribution, and ii) a
full numerical solution of the Boltzmann equation in phase-space. For
illustration, we apply these methods to the case of Scalar Singlet dark matter.
We explicitly show that even in this simple model the prediction for the dark
matter abundance can be affected by up to one order of magnitude compared to
the traditional treatment.
