Dark Matter Relic Abundance and Light Sterile Neutrinos

In this paper, we calculate the relic abundance of the dark matter particles when they can annihilate into sterile neutrinos with the mass $\lesssim 100 \text{ GeV}$ in a simple model. Unlike the usual standard calculations, the sterile neutrino may fall out of the thermal equilibrium with the thermal bath before the dark matter freezes out. In such a case, if the Yukawa coupling $y_N$ between the Higgs and the sterile neutrino is small, this process gives rise to a larger $\Omega_{\text{DM}} h^2$ so we need a larger coupling between the dark matter and the sterile neutrino for a correct relic abundance.