Extended Einstein-Dirac-aether theory: Spinor modifications of the dynamic aether kinetic term

In the framework of the Einstein-Dirac-aether theory the extended model is established, in which the backreaction of the spinor field on the unit vector field, describing the dynamic aether, is taken into account. For this purpose, we extended the Jacobson constitutive tensor, which enters the kinetic part of the Lagrangian of the unit vector (aetheric) field, by the terms containing spinor tensors and pseudotensors. The self-consistent system of master equations for the unit vector field, as well as, the spinor and gravitational fields is derived using the variation formalism in the framework of the effective field theory up to the second order in derivatives.