Axionic extension of the Einstein-aether theory

TL;DR

This paper extends Einstein-aether theory by incorporating axionic dark matter, analyzing new interactions via an effective field approach, and exploring cosmological solutions with diverse asymptotic behaviors.

Contribution

It introduces a comprehensive axion-aether interaction Lagrangian up to second order derivatives, expanding the theoretical framework of Einstein-aether models.

Findings

Derived new exact cosmological solutions with Big Rip, Pseudo Rip, and de Sitter behaviors.

Formulated the interaction terms based on irreducible parts of the aether's covariant derivative.

Provided a theoretical basis for axion-aether coupling in cosmological contexts.

Abstract

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.