Possible violation of the spin-statistics relation for neutrinos: cosmological and astrophysical consequences

We assume that the Pauli exclusion principle is violated for neutrinos, and consequently, neutrinos obey the Bose-Einstein statistics. Cosmological and astrophysical consequences of this assumption are considered. Neutrinos may form cosmological Bose condensate which accounts for all (or a part of) the dark matter in the universe. ``Wrong'' statistics of neutrinos could modify big bang nucleosynthesis, leading to the effective number of neutrino species smaller than three. Dynamics of the supernova collapse would be influenced and spectra of the supernova neutrinos may change. The presence of neutrino condensate would enhance contributions of the Z-bursts to the flux of the UHE cosmic rays and lead to substantial refraction effects for neutrinos from remote sources. The Pauli principle violation for neutrinos can be tested in the two-neutrino double beta decay.