Neutrino Dispersion in Magnetized Media and Spin Oscillations in the Early Universe

Abstract

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 $B\simleq T^2$, the neutrino refractive index in the early Universe is dominated by the standard ``non-local term''. If neutrinos are Dirac particles with magnetic moment $\mu$, then their right-handed components are thermally populated before the nucleosynthesis epoch by magnetically induced spin oscillations if $\mu B_0 \agt 10^{-6}\mu_{\rm B}\,{\rm gauss}$, where $\mu_{\rm B}=e/2m_e$ is the Bohr magneton and $B_0$ is a large-scale primordial magnetic field at $T_0\approx 1\,\rm MeV$. For a typically expected random field distribution, even smaller values for $\mu B_0$ would suffice to thermalize the right-handed Dirac components.