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 d kappa epends on a single Fermi - Bose parameter , and interpolates continuously between the bosonic and fermionic distributions when. changes from - 1 to + 1. We consider modi. cation 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 He-4 (which is equivalent to a decrease of the effective number of neutrinos by Delta N-nu approximate to - 0.6), + 2.6% for H-2, and - 7% for Li-7. 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.