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↔ bar 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 μm must be less than 3x10-5 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