Constraints on almost-Dirac neutrinos from neutrino-antineutrino oscillations

If a neutrino has both Dirac and Majorana masses (m,{μ}), as some recent models predict, {ν}{}{ν}{} oscillations within a single generation may cause a violation of the nucleosynthesis bound on the number of light neutrino species. Taking into account the effects of finite temperature and density, we find that {μ}m must be less than 3×{}10^-5 eV², which is too small to explain atmospheric neutrino observations. The bound can be softened to 0.05 eV² if the right-handed components couple to massless bosons (Majorons). We introduce a simple but quantitatively accurate formalism for tracking the approach of the sterile state to thermal equilibrium.