Standard model contributions to the neutrino index of refraction in the early Universe.

1 With the standard electroweak interactions, the lowest-order coherent forward scattering amplitudes of neutrinos in a CP symmetric medium (such as the early universe) are zero, and the index of refraction of a propagating neutrino can only arise from the expansion of gauge boson propagators, from radiative corrections, and from new physics interactions. Motivated by nucleosynthesis constraints on a possible sterile neutrino (suggested by the solar neutrino deficit and a possible 17 keV neutrino), we calculate the standard model contributions to the neutrino index of refraction in the early universe, focusing on the period when the temperature was of the order of a few MeV. We find sizable radiative corrections to the tree level result obtained by the expansion of the gauge boson propaga-family mixing (if any), effects from different family scattering can be dominated by radiative corrections. The result for ν + γ → ν + γ is zero at one-loop level, even if neutrinos are massive. The cancellation of infrared divergence in a coherent process is also discussed.