Cosmological bounds on neutrino degeneracy improved by flavor oscillations

We study three-flavor neutrino oscillations in the early universe in the presence of neutrino chemical potentials. We take into account all effects from the background medium, i.e. collisional damping, the refractive effects from charged leptons, and in particular neutrino self-interactions that synchronize the neutrino oscillations. We find that effective flavor equilibrium between all active neutrino species is established well before the big-bang nucleosynthesis (BBN) epoch if the neutrino oscillation parameters are in the range indicated by the atmospheric neutrino data and by the large mixing angle (LMA) MSW solution of the solar neutrino problem. For the other solutions of the solar neutrino problem, partial flavor equilibrium may be achieved if the angle theta_13 is close to the experimental limit tan^2(theta_13)<0.065. In the LMA case, the BBN limit on the nu_e degeneracy parameter, |xi_nu|< 0.07, now applies to all flavors. Therefore, a putative extra cosmic radiation contribution from degenerate neutrinos is limited to such low values that it is neither observable in the large-scale structure of the universe nor in the anisotropies of the cosmic microwave background radiation. Existing limits and possible future measurements, for example in KATRIN, of the absolute neutrino mass scale will provide unambiguous information on the cosmic neutrino mass density, essentially free of the uncertainty of the neutrino chemical. potentials.