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.
