Relativistic effective degrees of freedom and quantum statistics of neutrinos

Abstract

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

Cosmological bounds on neutrino statistics

“…Here we follow previous works and take a purely phenomenological approach for neutrino statistics, described by a single continuous parameter κ ν which describes purely fermionic (κ ν = +1) and purely bosonic (κ ν = −1) neutrinos. Previous analyses have described the main effects of κ ν = 1 on the early Universe, in particular on Big Bang Nucleosynthesis (BBN) [6,8,9], including a change in the contribution to the relativistic degrees of freedom (see also [10][11][12]). A modified neutrino statistics would also lead to a different behaviour as hot dark matter [13,14] and, in the extreme case of bosonic relic neutrinos, even as light as axions, they could condense and act as the cosmological dark matter [6].…”