Neutrino oscillations in the early universe: How large lepton asymmetry can be generated?

TL;DR

This paper analytically investigates how active-sterile neutrino oscillations in the early universe can generate lepton asymmetry, showing it is limited for small mass differences but can be significant for very large ones.

Contribution

It provides an analytical calculation of lepton asymmetry generation via neutrino oscillations, highlighting the impact of mass differences and refraction effects.

Findings

Lepton asymmetry can increase up to 6 orders of magnitude for small mass differences.

Refraction index back-reaction limits asymmetry growth at small mass differences.

Significant asymmetry (>0.1) is possible only for very large mass differences (~10^9 eV^2).

Abstract

The lepton asymmetry that could be generated in the early universe through oscillations of active to sterile neutrinos is calculated (almost) analytically for small mixing angles, sin 2\theta < 10^{-2}. It is shown that for a mass squared difference, \delta m^2=-1 eV^2 it may rise at most by 6 orders of magnitude from the initial ``normal'' value of 10^{-10}, since the back-reaction from the refraction index terminates this rise while the asymmetry is still small. Only for very large mass differences, \delta m^2 about 10^9 eV^2, the lepton asymmetry could reach a significant magnitude exceeding 0.1.