Appearance of neutrino asymmetries in the process of expansion of the Universe, hierarchy of neutrino masses and CP violation

Abstract

In this work, we study the appearance of neutrino asymmetries during the expansion of the Universe. A mathematical model based on differential equations was used to describe the processes of neutrino oscillations considering CP violation and neutrino collisions. An analysis of the emergence of neutrino asymmetry due to collisions of neutrinos with each other and due to CP violation during neutrino oscillations is presented. It was discovered that the asymmetry bifurcates into two states with positive and negative asymmetry for the inverse hierarchy of neutrino masses. A state with a normal hierarchy of neutrino masses is unstable and is not realized. It is shown that the maximum CP violation is realized. The influence of this process on the dispersion of the primordial $^4\text{He}$ mass fraction is calculated, which is confirmed by astrophysical observations. Thus, the inverse hierarchy of neutrino masses is realized. The CP violation in neutrino oscillations is maximum and the phase is $\delta_{13}=270^\circ (-\pi/2)$