Non-Minimal Einstein-Dirac-Axion Theory: Spinorization of the Early Universe Induced by Curvature

A new non-minimal version of the Einstein-Dirac-axion theory is established. This version of the non-minimal theory describing the interaction of gravitational, spinor and axion fields is of the second order in derivatives in the context of the Effective Field Theory, and is of the first order in the spinor particle number density. The model Lagrangian contains four parameters of the non-minimal coupling and includes, in addition to the Riemann, Ricci tensor and Ricci scalar, the left-dual and right-dual curvature tensors. The pseudoscalar field appears in the Lagrangian in terms of trigonometric functions providing the discrete symmetry associated with axions is supported. The coupled system of extended master equations for the gravitational, spinor and axion fields is derived; the structure of new non-minimal sources appeared in these master equations is discussed. Application of the established theory to the isotropic homogeneous cosmological model is considered; new exact solutions are presented for a few model sets of guiding non-minimal parameters. A special solution is presented, which describes an exponential growth of the spinor number density; this solution shows that spinor particles (massive fermions and massless neutrinos) can be born in early Universe due to the non-minimal interaction with the space-time curvature.