  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.
