Neutrino Oscillations and Cosmology

Phenomenology of neutrino oscillations in vacuum and in cosmological plasma is considered. Neutrino oscillations in vacuum are usually described in plane wave approximation. In this formalism there is an ambiguity if one should assume $\delta p =0$ and correspondingly $\delta E\neq 0$ or vice versa $\delta E =0$ and $\delta p \neq 0$, or some other condition. We will use the standard set of quantum field theory rules and show that the theoretical description is unambiguous and that the state of oscillating neutrinos is determined by the conditions of their registration. The wave packet formalism is a natural result of such an approach. Oscillating neutrinos in cosmological plasma cannot be described in terms of wave function because of a fast loss of coherence due to elastic or inelastic scattering, so that one should use the density matrix formalism. Kinetic equations for the density matrix of oscillating neutrinos are derived. Numerical and semi-analytical solutions of the equations are examined. In particular, a possibility of amplification of cosmological lepton asymmetry in the sector of active neutrinos mixed to sterile ones is critically discussed.