Remarks on the cosmic density of degenerate neutrinos

We reinvestigate the evolution of strongly degenerate neutrinos in the early universe. With the larger degeneracy, the neutrino number freezes at higher temperatures because the neutrino annihilation rate decreases. We consider a very large degeneracy, so large that the neutrino number freezes before the events in which the particle degrees of freedom in the universe decrease (e.g., the muon annihilation and the quark-hadron phase transition). In such a case, the degeneracy by the time of nucleosynthesis becomes smaller than the initial degeneracy. We calculate how much it decreases from the initial value on the basis of the conservation of the neutrino number and the total entropy. We find a large drop in the degeneracy, but it is not large enough to affect the current constraints on the neutrino degeneracy from big bang nucleosynthesis and cosmic microwave background