Extension of the Einstein–Dirac-axion-aether theory based on an effective metric with a spinor kernel

In this paper, we consider an axionic extension of the Einstein–Dirac-aether theory, which is based on the spinor modification of the kinetic term of the pseudoscalar field and describes the backreaction of the spinor field on the axionic dark matter. The main instrument of this extension is the effective metric constructed using the aether velocity four-vector and a kernel, which depends on the basic spinor scalar and on the square of the basic spinor pseudoscalar. The periodic potential of the axion field includes a guiding function, which regulates the dynamics of axions and predetermines the properties of their equilibrium states. This guiding function and the kernel of the effective metric, as well, are considered to be functions of the expansion scalar of the aether flow. The master equation for the guiding function is obtained as a consequence of the Lagrangian invariance with respect to the discrete transformations prescribed by the axion field shift symmetry. The self-consistent set of coupled master equations is derived, which includes new source-terms in the modified master equations for the spinor, axion, vector and gravitational fields. Cosmological applications of the extended theory are considered; new exact solutions of these equations are presented for the isotropic homogeneous model of the Universe evolution. Discussion is focused on the mechanism of backreaction of the spinor field on the axionic dark matter evolution.