Relic neutrino asymmetry evolution from first principles

TL;DR

The paper addresses how light sterile (and mirror) neutrinos can generate relic lepton asymmetries through active-sterile oscillations in the early universe, with significant implications for Big Bang Nucleosynthesis and sterile-neutrino cosmology. Starting from the exact Quantum Kinetic Equations for a two-flavour system, the authors develop a systematic hierarchy of approximations that extend the adiabatic treatment to include decoherence from collisions and derive explicit expressions for the decoherence $D$ and repopulation $R$ terms, as well as the momentum dependence through $a(p)$ and $b(p)$. They derive an explicit non-linear lepton-number evolution equation for $L_\alpha$ (Lev4) and show how the static/adiabatic picture emerges as a first-principles limit, thereby validating earlier approximations. The analysis is then extended to three flavours via momentum-averaged Quantum Rate Equations, revealing a quasi-decoupling into two two-flavour subsystems (e.g., $\nu_{\tau}-\nu_s$ and $\nu_{\mu}-\nu_s$) with inter-subsystem coupling only through Wolfenstein terms, and it discusses mirror neutrinos and region-of-applicability to map out when simple two-flavour pictures suffice and when genuine multi-flavour effects become important.

Abstract

The exact Quantum Kinetic Equations for a two-flavour active-sterile neutrino system are used to provide a systematic derivation of approximate evolution equations for the relic neutrino asymmetry. An extension of the adiabatic approximation for matter-affected neutrino oscillations is developed which incorporates decoherence due to collisions. Exact and approximate expressions for the decoherence and repopulation functions are discussed. A first pass is made over the exact treatment of multi-flavour partially incoherent oscillations.