Scalar induced resonant sterile neutrino production in the early Universe

It has been recently suggested \cite{Bezrukov:2017ike,Bezrukov:2018wvd} that a cosmic scalar field can completely change the keV-scale sterile neutrino production in the early Universe. Its effect may, for various parameter choices, either suppress sterile neutrino production and make moderate active-sterile mixing cosmologically acceptable, or increase the production and generate considerable dark matter component out of sterile neutrino with otherwise negligible mixing with SM. In this paper we provide analytic estimates complementing and providing details of the numerical calculations performed in \cite{Bezrukov:2018wvd} in the case of resonant amplification of the sterile neutrino production. We also discuss phenomenological and theoretical issues related to the successful implementation of this idea in fully realistic extensions of the Standard Model of particle physics.