Relativistic effective degrees of freedom and quantum statistics of neutrinos

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.