Neutrino dispersion in magnetized media and spin oscillations in the early Universe

We derive general expressions for the neutrino dispersion relation in a magnetized plasma with a wide range of temperatures, chemical potentials, and magnetic field strengths. If the electron and proton chemical potentials vanish, as in the early Universe, there is no magnetization contribution to the neutrino refractive index to leading order in the Fermi coupling constant, contrary to claims in the recent literature. Therefore, as long as the magnetic field satisfies Bor∼10-6μB G, where μB=e/2me is the Bohr magneton and B0 is a large-scale primordial magnetic field at T0∼1 MeV. For a typically expected random field distribution, even smaller values for μB0 would suffice to thermalize the right-handed Dirac components. (orig.)