Strong coupling in Horava gravity

TL;DR

This paper analyzes the perturbative stability of Horava gravity, revealing two distinct strong coupling issues that prevent it from recovering General Relativity in the infrared, challenging its viability as a quantum gravity candidate.

Contribution

It identifies and explains two strong coupling problems in Horava gravity, showing they persist regardless of modifications, thus questioning the theory's consistency with observed gravitational phenomena.

Findings

Two strong coupling problems identified in Horava gravity.

Breaking detailed balance can evade one problem but not the other.

Theory likely incompatible with experimental tests of General Relativity.

Abstract

By studying perturbations about the vacuum, we show that Horava gravity suffers from two different strong coupling problems, extending all the way into the deep infra-red. The first of these is associated with the principle of detailed balance and explains why solutions to General Relativity are typically not recovered in models that preserve this structure. The second of these occurs even without detailed balance and is associated with the breaking of diffeomorphism invariance, required for anisotropic scaling in the UV. Since there is a reduced symmetry group there are additional degrees of freedom, which need not decouple in the infra-red. Indeed, we use the Stuckelberg trick to show that one of these extra modes become strongly coupled as the parameters approach their desired infra-red fixed point. Whilst we can evade the first strong coupling problem by breaking detailed balance, we cannot avoid the second, whatever the form of the potential. Therefore the original Horava model, and its "phenomenologically viable" extensions do not have a perturbative General Relativity limit at any scale. Experiments which confirm the perturbative gravitational wave prediction of General Relativity, such as the cumulative shift of the periastron time of binary pulsars, will presumably rule out the theory.