Cosmic alignment of the aether

TL;DR

This paper studies the stability of the aether field in Einstein-aether and Horava gravity under large deviations from isotropy, revealing conditions for relaxation or runaway behavior depending on initial anisotropy and coupling constants.

Contribution

It extends previous work by analyzing large anisotropic deviations in a homogeneous universe, identifying conditions for isotropization or instability based on initial parameters.

Findings

Aether and metric tend to isotropize if initial deviations are small.

Large initial anisotropies can lead to runaway behavior or singularities.

Behavior depends critically on coupling constants and initial boost angles.

Abstract

In Einstein-aether theory and Horava gravity, a timelike unit vector is coupled to the spacetime metric. It has previously been shown that in an exponentially expanding homogeneous, isotropic background, small perturbations of the vector relax back to the isotropic frame. Here we investigate large deviations from isotropy, maintaining homogeneity. We find that, for generic values of the coupling constants, the aether and metric relax to the isotropic configuration if the initial aether hyperbolic boost angle and its time derivative in units of the cosmological constant are less than something of order unity. For larger angles or angle derivatives, the behavior is strongly dependent on the values of the coupling constants. Generally there is runaway behavior, in which the anisotropy increases with time, and/or singularities occur.