Dodelson-Widrow production of sterile neutrino Dark Matter with non-trivial initial abundance

The simplest way to create sterile neutrinos in the early Universe is by their admixture to active neutrinos. However, this mechanism, connected to the Dark Matter (DM) problem by Dodelson and Widrow (DW), cannot simulatenously meet the relic abundance constraint as well as bounds from structure formation and X-rays. Nonetheless, unless a symmetry forces active-sterile mixing to vanish exactly, the DW mechanism will unavoidably affect the sterile neutrino DM population created by any other production mechanism. We present a semi-analytic approach to the DW mechanism acting on an arbitrary initial abundance of sterile neutrinos, allowing to combine DW with any other preceeding production mechanism in a physical and precise way. While previous analyses usually assumed that the spectra produced by DW and another mechanism can simply be added, we use our semi analytic results to discuss the validity of this assumption and to quantify its accurateness, thereby also scrutinising the DW spectrum and the derived mass bounds. We then map our results to the case of sterile neutrino DM from the decay of a real SM singlet coupled to the Higgs. Finally, we will investigate aspects of structure formation beyond the usual simple free-streaming estimates in order to judge on the effects of the DW modification on the sterile neutrino DM spectra generated by scalar decay.