Inhomogeneous spacetimes in Einstein-\ae ther Cosmology

TL;DR

This paper explores inhomogeneous Szekeres and FLRW-like spacetimes within Einstein-e6ther theory, revealing specific conditions for their existence and analyzing their stability, showing richer dynamics than in General Relativity.

Contribution

It derives new inhomogeneous solutions in Einstein-e6ther theory and examines their stability, extending understanding of cosmological models in this modified gravity framework.

Findings

Inhomogeneous Szekeres solutions exist under specific coupling conditions.

A class of inhomogeneous FLRW-like spacetimes is permitted for arbitrary coupling.

Solutions exhibit more complex evolution compared to General Relativity, with diverse attractors.

Abstract

We investigate the existence of inhomogeneous Szekeres spacetimes in Einstein-\ae ther theory. We show that inhomogeneous solutions which can be seen as extension of the Szekeres solutions existing in Einstein-\ae ther gravity only for a specific relation between the dimensionless coefficients which defines the coupling between the \ae ther filed with gravity. The two Szekeres classes of solutions are derived. Also a class of inhomogeneous FLRW-like spacetimes is allowed by the theory for arbitrary values of the dimensionless coefficients of the \ae ther field. The stability of the solutions obtained is performed from where we find that the field equations evolve more variously in Einstein-\ae ther than in General Relativity, where isotropic spacetimes and Kantowski-Sachs spacetimes are found to be attractors.