  Kinetic decoupling of dark matter typically happens much later than chemical
freeze-out. In fact, local thermal equilibrium is an important assumption for
the usual relic density calculations based on solving the Boltzmann equation
(for its 0-th moment) describing the dark matter number density. But is this
assumption always justified? Here we address this question and discuss the
consequences of more accurate treatments. The first treatment is relying on the
inclusion of higher moments of the Boltzmann equation and the second on solving
the evolution of the phase-space distribution function fully numerically. For
illustration, these methods are applied to the Scalar Singlet model, often
referred to as the simplest WIMP DM possibility from a model-building
perspective. It is explicitly shown that even in this simple model the
prediction for the dark matter abundance can be affected by as much as one
order of magnitude.
