Gravity with a dynamical preferred frame

TL;DR

This paper explores a covariant gravity model with a dynamical preferred frame, analyzing its implications for Lorentz invariance violation, vacuum solutions, and potential singularities, while proposing modifications to address theoretical limitations.

Contribution

It introduces a covariant aether model with antisymmetrized derivatives, linking it to Einstein-Maxwell-charged dust, and discusses its solutions and singularity issues.

Findings

Model includes all vacuum solutions of general relativity

Aether exhibits two massless transverse excitations

Gradient singularities indicate breakdown of the effective theory

Abstract

We study a generally covariant model in which local Lorentz invariance is broken "spontaneously" by a dynamical unit timelike vector field $u^a$---the "aether". Such a model makes it possible to study the gravitational and cosmological consequences of preferred frame effects, such as ``variable speed of light" or high frequency dispersion, while preserving a generally covariant metric theory of gravity. In this paper we restrict attention to an action for an effective theory of the aether which involves only the antisymmetrized derivative $\nabla_{[a}u_{b]}$. Without matter this theory is equivalent to a sector of the Einstein-Maxwell-charged dust system. The aether has two massless transverse excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions). However, the aether generally develops gradient singularities which signal a breakdown of this effective theory. Including the symmetrized derivative in the action for the aether field may cure this problem.