# Relativistic effective degrees of freedom and quantum statistics of neutrinos

## TL;DR

This paper derives analytical formulas for the relativistic effective degrees of freedom considering neutrinos with mixed quantum statistics and shows that lepton asymmetries can influence these degrees.

## Contribution

It provides new analytical expressions for $g_\ast$ with non-pure fermionic neutrinos and explores their dependence on lepton flavor asymmetries.

## Key findings

- $g_\ast$ can be larger with fermionic neutrinos than bosonic ones under certain conditions.
- Lepton flavor asymmetries significantly affect the effective degrees of freedom.
- Analytical expressions facilitate better understanding of neutrino contributions in cosmology.

## Abstract

Analytical expressions of the relativistic effective degrees of freedom $g_\ast$ with non-pure fermionic neutrinos are presented. A semi-analytical study is performed to show that $g_\ast$ with pure fermionic neutrinos may be greater than $g_\ast$ with pure bosonic neutrinos for non-vanishing lepton flavor asymmetries.