Complete Classification of Analytical Models in Einstein-Aether Cosmology

TL;DR

This paper systematically classifies all analytical solutions of FLRW cosmologies within Einstein-aether theory, comparing them to General Relativity and identifying models unaffected by the aether field.

Contribution

It provides a complete analytical classification of Einstein-aether cosmological models, revealing that the aether field does not alter the qualitative dynamics in most cases.

Findings

Aether scales geometric and dynamical parameters without changing qualitative behavior.

Eight models are unaffected by the aether, showing no cosmological influence.

Results are consistent with and extend previous understanding of Einstein-aether cosmologies.

Abstract

We present all possible analytical solutions of the Friedmann-Lema\^itre-Robertson-Walker metric in Einstein-aether theory for all values of the cosmological constant and spatial curvature with many reasonable values of the equation-of-state parameter. We analyze the dynamics of each model analytically and also graphically by plotting the geometric radius, Hubble and deceleration parameters along with the effective energy conditions. All our results are compared with the corresponding models in General Relativity. The two key results are (i) the aether does not qualitatively change the dynamics of the cosmological models but merely scales the geometric radius, Hubble, and deceleration parameters, and (ii) we found eight models that are entirely void of any aether, meaning in such a universe aether does not play any role cosmologically, although it affects the solar system dynamics.