Neutrino oscillation in an anisotropic cosmological model

The determining factor for the physics of processes and for the expansion dynamics of Universe in the anisotropic cosmological model is the behavior of neutrinos and antineutrinos of all kinds during a sharp anisotropic expansion at a time when the temperature has dropped so much that processes with neutrinos are already proceeding rather slowly compared to the rate of change of the system parameters and the thermodynamic equilibrium for neutrinos is broken. It is assumed that after a certain moment the probability of interaction of neutrinos with other particles and between itself is small, neutrinos become free. In this case, the component of the neutrino momentum along the axis at which compression occur increases due to the "blue" shift. The distribution of neutrino momentum becomes sharply anisotropic, elongated in the direction of compression, and the energy of each neutrino increases. In this stage, the neutrinos generated by the mixing of mass and flavor oscillate. If right hand neutrinos and left hand antineutrinos exist, their interaction with matter should be much weaker than the weak interaction of the flavor left hand neutrinos and right hand antineutrinos should be "sterile" neutrinos. In this paper we consider the dynamics of neutrino oscillations associated with a homogeneous but anisotropic Universe within the framework of a stochastic model. Expressions are obtained for the mixing angles, probabilities, and lengths of three neutrino oscillations. The study of oscillation probabilities makes it possible to determine the hierarchy of neutrino masses and the violation of CP symmetry in the neutrino sector. The results obtained in this work clearly show that a phase shift of neutrino oscillations can appear depending on the anisotropy of space.