Vacuum solutions in the Einstein-Aether Theory

TL;DR

This paper derives and analyzes exact vacuum and fluid solutions in Einstein-Aether theory, highlighting differences from General Relativity and exploring the role of the aether field in cosmological dynamics and energy conditions.

Contribution

It provides new exact solutions in Einstein-Aether theory for FLRW symmetry, revealing unique singularities and the influence of the aether field on cosmological behavior.

Findings

Existence of solutions with singularities not present in GR.

The aether field affects the energy conditions and can drive accelerated expansion.

Solutions include bouncing, collapsing, and accelerating universe models.

Abstract

The Einstein-Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field, called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of perfect fluid, both with Friedmann-Lemaitre-Robertson-Walker (FLRW) symmetry: (i) a fluid with constant energy density ($p=-\rho_0$), and (ii) a fluid with zero energy density ($\rho_0=0$), corresponding to the vacuum solution with and without cosmological constant ($\Lambda$), respectively. Our solutions show that the EA and GR theories do not differentiate each other only by the coupling constants. This difference is clearly shown because of the existence of singularities that there are not in GR theory. This characteristic appears in the solutions with $p=-\rho_0$ as well as with $\rho_0=0$, where this last one depends only on the aether field. Besides, we consider the term of the EA theory in the Raychaudhuri equation and discuss the meaning of the strong energy condition in this scenario and found that this depends on aether field. The solutions admit an expanding or contracting system. A bounce, a singular, a constant and an accelerated expansion solutions were also obtained, exhibiting the richness of the EA theory from the dynamic point of view of a collapsing system or of a cosmological model. The analysis of energy conditions, considering an effective fluid shows that the term of the aether contributes significantly for the accelerated expansion of the system for the case in which the energy density is constant. On the other hand, for the vacuum case ($\rho_0=0$), the energy conditions are all satisfied for the aether fluid.