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 μm must be less than 3×${10}^{\mathrm{-}5}$ ${\mathrm{eV}}^2$, which is too small to explain atmospheric neutrino observations. The bound can be softened to 0.05 ${\mathrm{eV}}^2$ 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.