Active-sterile neutrino oscillations in the early Universe with full collision terms

TL;DR

This paper revisits sterile neutrino thermalisation in the early Universe by numerically solving quantum kinetic equations with full collision terms, revealing discrepancies with previous approximations and proposing a new improved scheme.

Contribution

It provides the first detailed numerical comparison of full collision terms with approximate methods in sterile neutrino thermalisation calculations.

Findings

Full collision term calculations show better agreement with some approximations than expected.

Identifies unphysical neutrino production and the importance of momentum redistribution through scattering.

Proposes a new approximation scheme that improves accuracy over previous methods.

Abstract

Sterile neutrinos are thermalised in the early Universe via oscillations with the active neutrinos for certain mixing parameters. The most detailed calculation of this thermalisation process involves the solution of the momentum-dependent quantum kinetic equations, which track the evolution of the neutrino phase space distributions. Until now the collision terms in the quantum kinetic equations have always been approximated using equilibrium distributions, but this approximation has never been checked numerically. In this work we revisit the sterile neutrino thermalisation calculation using the full collision term, and compare the results with various existing approximations in the literature. We find a better agreement than would naively be expected, but also identify some issues with these approximations that have not been appreciated previously. These include an unphysical production of neutrinos via scattering and the importance of redistributing momentum through scattering, as well as details of Pauli blocking. Finally, we devise a new approximation scheme, which improves upon some of the shortcomings of previous schemes.