Fermi-Boltzmann statistics of neutrinos and relativistic effective degrees of freedom

TL;DR

This paper studies how changing neutrino statistics from Fermi-Dirac to Maxwell-Boltzmann affects the early universe's relativistic degrees of freedom, revealing a decrease with larger lepton asymmetries and confirming the excess of neutrino effective number isn't fully explained by this change.

Contribution

It introduces a continuous transformation of neutrino statistics and analyzes its impact on the relativistic degrees of freedom in the early universe.

Findings

Relativistic degrees of freedom decrease with deviation from Fermi-Dirac neutrino statistics.

Changing neutrino statistics alone does not account for the excess in effective neutrino number.

The effect is significant in the presence of large lepton asymmetries.

Abstract

We investigate the effect of the presence of non-pure fermionic neutrinos on the relativistic effective degrees of freedom in the early universe. The statistics of neutrinos is transformed continuously from Fermi-Dirac to Maxwell-Boltzmann statistics. We find that the relativistic degrees of freedom decreases with the deviation from pure Fermi-Dirac statistics of neutrinos if there are constant and large lepton asymmetries. Additionally, we confirm that the change of the statistics of neutrinos from Fermi-Dirac to Maxwell-Boltzmann is not sufficient to cover the excess of the effective number of neutrinos.