Neutrino statistics and big bang nucleosynthesis

Neutrinos may possibly violate the spin-statistics theorem, and hence obey Bose statistics or mixed statistics despite having spin half. We find the generalized equilibrium distribution function of neutrinos which depends on a single fermi-bose parameter, \kappa, and interpolates continuously between the bosonic and fermionic distributions when \kappa changes from -1 to +1. We consider modification of the Big Bang Nucleosynthesis (BBN) in the presence of bosonic or partly bosonic neutrinos. For pure bosonic neutrinos the abundances change (in comparison with the usual Fermi-Dirac case) by -3.2% for 4He (which is equivalent to a decrease of the effective number of neutrinos by \Delta N_\nu = - 0.6), +2.6% for 2H and -7% for 7Li. These changes provide a better fit to the BBN data. Future BBN studies will be able to constrain the fermi-bose parameter to \kappa > 0.5, if no deviation from fermionic nature of neutrinos is found. We also evaluate the sensitivity of future CMB and LSS observations to the fermi-bose parameter.