Maximum lepton asymmetry from active-sterile neutrino oscillations in the early Universe

A large lepton asymmetry could be generated in the early Universe by oscillations of active to sterile neutrinos with a small mixing angle sin 2 theta <10(-2). The final order of magnitude of the lepton asymmetry <eta> is mainly determined by its growth in the last stage of evolution when the Mikheyev-Smirnov-Wolfenstein resonance dominates the kinetic equations. In this paper we present a simple way of calculating the maximum possible lepton asymmetry which can be created. Our results are in good agreement with previous calculations. Furthermore, we find that the growth of asymmetry does not obey any particular power law. We find that the maximum possible asymmetry at the freeze-out of the n/p ratio at T similar to1 MeV strongly depends on the mass-squared difference deltam(2): the asymmetry is negligible for \ deltam(2)\ much less than1 eV(2) and reaches asymptotically large values for \ deltam(2)\ greater than or similar to 50 eV(2).