Sterile neutrino Dark Matter production from scalar decay in a thermal bath

We calculate the production rate of singlet fermions from the decay of neutral or charged scalar fields in a hot plasma. We find that there are considerable thermal corrections when the temperature of the plasma exceeds the mass of the decaying scalar. We give analytic expressions for the temperature-corrected production rates in the regime where the decay products are relativistic. We also study the regime of non-relativistic decay products numerically. Our results can be used to determine the abundance and momentum distribution of Dark Matter particles produced in scalar decays. The inclusion of thermal corrections helps to improve predictions for the free streaming of the Dark Matter particles, which is crucial to test the compatibility of a given model with cosmic structure formation. With some modifications, our results may be generalised to the production of other Dark Matter candidates in scalar decays.