Fermi-Boltzmann statistics of neutrinos and relativistic effective   degrees of freedom
  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. 
Jun Iizuka and Teruyuki Kitabayashi
hep-ph