On the applicability of approximations used in calculation of spectrum
  of Dark Matter particles produced in particle decays
  For the Warm Dark Matter (WDM) candidates the momentum distribution of
particles becomes important, since it can be probed with observations of
Lyman-$\alpha$ forest structures and confronted with coarse grained phase space
density in galaxy clusters. We recall the calculation bt Kaplinghat (2005) of
the spectrum in case of dark matter non-thermal production in decays of heavy
particles emphasizing on the inherent applicability conditions, which are
rather restrictive and sometimes ignored in literature. Cold part of the
spectrum requires special care when WDM is considered.
