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We study the production of sterile neutrinos in the region $T\sim M_W$ in anextension beyond the standard model with the see-saw mass matrix originating inYukawa couplings to Higgs-like scalars with masses and vev's of the order ofthe electroweak scale. Sterile neutrinos are produced by the decay of scalarsand standard model vector bosons. We obtain the index of refraction, dispersionrelations, mixing angles in the medium and production rates including those forright-handed sterile neutrinos, from the standard model and beyond the standardmodel self-energies. For $1 \lesssim M_W/T \lesssim 3$ we find narrow MSWresonances with $k \lesssim T$ for both left and right handed neutrinos even inabsence of a lepton asymmetry in the (active) neutrino sector, as well as verylow energy ($k/T \ll |\xi|$) narrow MSW resonances in the presence of a leptonasymmetry consistent with the bounds from WMAP and BBN. For small vacuum mixingangle, consistent with observational bounds, the absorptive part of theself-energies lead to a strong damping regime very near the resonancesresulting in the \emph{exact} degeneracy of the propagating modes with aconcomitant breakdown of adiabaticity. We argue that cosmological expansionsweeps through the resonances, \emph{resonant and non-resonant} sterileneutrino production results in a highly \emph{non-thermal} distributionfunction enhanced at small momentum $k < T$, with potentially importantconsequences for their free streaming length and transfer function at smallscales.

Sterile neutrinos produced near the EW scale I: mixing angles, MSW resonances and production rates