Lessons from the decoupling limit of Horava gravity

TL;DR

This paper investigates the decoupling limit of Horava gravity, analyzing the strong coupling problem, the necessity of Lorentz violation at low scales, and the implications for energy conservation and the Equivalence Principle.

Contribution

It demonstrates the conditions under which the Stuckelberg field couples to energy violation and explores the phenomenological consequences of Lorentz violation in Horava gravity.

Findings

Strong coupling persists without low-scale Lorentz violation.

Coupling to energy violation affects force between particles.

Potential to constrain Lorentz violation scale through equivalence principle tests.

Abstract

We consider the so-called "healthy" extension of Horava gravity in the limit where the Stuckelberg field decouples from the graviton. We verify the alleged strong coupling problem in this limit, under the assumption that no large dimensionless parameters are put in by hand. This follows from the fact that the dispersion relation for the Stuckelberg field does not have the desired z = 3 anisotropic scaling in the UV. To get the desired scaling and avoid strong coupling one has to introduce a low scale of Lorentz violation and retain some coupling between the graviton and the Stuckelberg field. We also make use of the foliation preserving symmetry to show how the Stuckelberg field couples to some violation of energy conservation. We source the Stuckelberg field using a point particle with a slowly varying mass and show that two such particles feel a constant attractive force. In this particular example, we see no Vainshtein effect, and violations of the Equivalence Principle. The latter is probably generic to other types of source and could potentially be used to place lower bounds on the scale of Lorentz violation.