Gravity with a dynamical preferred frame

TL;DR

The paper develops a generally covariant gravity theory with a dynamical unit timelike vector field $u^a$ (the aether) that defines a preferred frame and breaks local Lorentz invariance in a controlled way. In the minimal antisymmetric-derivative model, the theory reproduces a sector of Einstein-Maxwell-charged dust, contains two massless transverse excitations, and generically develops gradient singularities that may be cured by including the symmetric derivative term. The authors classify exact and linearized solutions, including spherically symmetric spacetimes with an aether charge, and analyze the linearized spectrum, revealing additional propagating modes beyond the usual graviton. They also study matter couplings up to dimension four and beyond, showing how Lorentz-violating operators modify propagation and can yield high-frequency dispersion or variable light speeds, with implications for cosmology and astrophysical observations.

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.