Variations on an aethereal theme

TL;DR

This paper surveys Lorentz-violating gravity theories involving a preferred aether field, examining how breaking diffeomorphism invariance affects their structure and degrees of freedom, with implications for phenomenology like dark matter behavior.

Contribution

It provides a comprehensive analysis of the structure and consequences of Lorentz-violating gravity theories with aether fields, highlighting the effects of broken diffeomorphism invariance.

Findings

Different constructions of the aether lead to novel degrees of freedom.

Breaking diffeomorphism invariance introduces background structures like folations and clocks.

Theories with a background clock can mimic dark matter properties.

Abstract

We consider a class of Lorentz-violating theories of gravity involving a timelike unit vector field (the aether) coupled to a metric, two examples being Einstein-aether theory and Ho\v{r}ava gravity. The action always includes the Ricci scalar of the metric and the invariants quadratic in covariant derivatives of the aether, but the theories differ in how the aether is constructed from other fields, and whether those fields are varied in the action. Fields that are not varied define background structures breaking diffeomorphsim invariance, including threadings, folations, and clocks, which generally produce novel degrees of freedom arising from the violation of what would otherwise be initial value constraints. The principal aims of this paper are to survey the nature of the theories that arise, and to understand the consequences of breaking diffeomorphism invariance in this setting. In a companion paper [arXiv:1504.03305], we address some of the phenomenology of the "ponderable aether" case in which the presence of a background clock endows the aether with a variable internal energy density that behaves in some respects like dark matter.