Axionic extension of the Einstein-aether theory
  We extend the Einstein-aether theory to take into account the interaction
between a pseudoscalar field, which describes the axionic dark matter, and a
time-like dynamic unit vector field, which characterizes the velocity of the
aether motion. The Lagrangian of the Einstein-aether-axion theory includes
cross-terms based on the axion field and its gradient four-vector, on the
covariant derivative of the aether velocity four-vector, and on the Riemann
tensor and its convolutions. We follow the principles of the Effective Field
theory, and include into the Lagrangian of interactions all possible terms up
to the second order in the covariant derivative. Interpretation of new
couplings is given in terms of irreducible parts of the covariant derivative of
the aether velocity, namely, the acceleration four-vector, the shear and
vorticity tensors, and the expansion scalar. A spatially isotropic and
homogeneous cosmological model with dynamic unit vector field and axionic dark
matter is considered as an application of the established theory; new exact
solutions are discussed, which describe models with a Big Rip, Pseudo Rip and
de Sitter-type asymptotic behavior.
