On the Extra Mode and Inconsistency of Horava Gravity

TL;DR

This paper investigates the consistency issues of Horava gravity, revealing an extra scalar mode that causes instabilities and strong coupling problems, questioning the theory's viability as a quantum gravity candidate.

Contribution

It identifies and analyzes the problematic scalar mode in Horava gravity, highlighting its instabilities and low strong coupling scale, and clarifies subtleties in the Stueckelberg formalism application.

Findings

The extra scalar mode exhibits exponential instabilities.

The mode becomes strongly coupled at a low cutoff scale.

The projectable version relates to ghost condensate but remains problematic.

Abstract

We address the consistency of Horava's proposal for a theory of quantum gravity from the low-energy perspective. We uncover the additional scalar degree of freedom arising from the explicit breaking of the general covariance and study its properties. The analysis is performed both in the original formulation of the theory and in the Stueckelberg picture. A peculiarity of the new mode is that it satisfies an equation of motion that is of first order in time derivatives. At linear level the mode is manifest only around spatially inhomogeneous and time-dependent backgrounds. We find two serious problems associated with this mode. First, the mode develops very fast exponential instabilities at short distances. Second, it becomes strongly coupled at an extremely low cutoff scale. We also discuss the "projectable" version of Horava's proposal and argue that this version can be understood as a certain limit of the ghost condensate model. The theory is still problematic since the additional field generically forms caustics and, again, has a very low strong coupling scale. We clarify some subtleties that arise in the application of the Stueckelberg formalism to Horava's model due to its non-relativistic nature.