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.Comment: 11 pages, 3 figures, matches version in JCAP, discussion and references extended slightl

Paradoxes of neutrino oscillations

Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss, in the framework of the wave packet approach, a number of such issues, including the relevance of the "same energy" and "same momentum" assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the production/detection and propagation coherence conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillation probabilities on the neutrino production and detection processes, the applicability limits of the stationary source approximation, and Lorentz invariance of the oscillation probability. We also develop a novel approach to calculation of the oscillation probability in the wave packet picture, based on the summation/integration conventions different from the standard one, which gives a new insight into the oscillation phenomenology. We discuss a number of apparently paradoxical features of the theory of neutrino oscillations.Comment: LaTeX, 45 pages, no figures. v2: references adde

Models of Neutrino Masses and Baryogenesis

Majorana masses of the neutrino implies lepton number violation and is intimately related to the lepton asymmetry of the universe, which gets related to the baryon asymmetry of the universe in the presence of the sphalerons during the electroweak phase transition. Assuming that the baryon asymmetry of the universe is generated before the electroweak phase transition, it is possible to dicriminate different classes of models of neutrino masses. While see-saw mechanism and the triplet higgs mechanism are preferred, the Zee-type radiative models and the R-parity breaking models requires additional inputs to generate baryon asymmetry of the universe during the electroweak phase transition.Comment: 27 pages including 5 figures; Review article for Pramana: the Indian Journal of Physic