Analytical treatment of neutrino asymmetry equilibration from flavour oscillations in the early universe
Yvonne Y. Y. Wong
TL;DR
The paper investigates whether large relic neutrino asymmetries can equilibrate among active flavours before BBN, building on prior numerical work with an analytic framework that emphasizes collective oscillations driven by nonlinear self-interactions. It develops a two-flavour treatment that yields a non-dissipative, MSW-like collective transition and then outlines a qualitative three-flavour extension, highlighting how initial asymmetries and mixing parameters shape the outcome. The results show that, for maximal mixing and LMA-like solar parameters, complete equilibration before BBN is robust, while nonmaximal mixing requires collisional damping to achieve substantial equilibration. In the three-flavour case, theta13 can induce partial equilibration prior to BBN via additional resonances, though the final outcome remains sensitive to the treatment of active-active collisions. Overall, the work clarifies how flavour dynamics could propagate electron-neutrino constraints to all flavours and underscores the role of collisional physics and mixing angles in early-Universe neutrino evolution.
Abstract
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 $θ_{13}$ 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.