Analytical treatment of neutrino asymmetry equilibration from flavour oscillations in the early universe

A recent numerical study by A. D. Dolgov, S. H. Hansen, S. Pastor, S. T. Petcov, G. G. Raffelt, and D. V. Semikoz (DHPPRS) [hep-ph/0201287] found that complete or partial equilibrium between all active neutrino flavours can be achieved before the big bang nucleosynthesis epoch via flavour oscillations, if the oscillation parameters are those inferred from the atmospheric and solar neutrino data, and, in some cases, if $\theta_{13}$ is also sizeable. As such, cosmological constraints on the electron neutrino-antineutrino asymmetry are now applicable in all three neutrino sectors. In the present work, we provide an analytical treatment of the scenarios considered in DHPPRS, and demonstrate that their results are stable even for very large initial asymmetries. The equilibration mechanism can be understood in terms of an MSW-like effect for a maximally mixed and effectively monochromatic system. We also comment on DHPPRS's choices of mixing parameters, and their handling of collisional effects, both of which could impinge on the extent of flavour equilibrium.