Relativistic Quantum Gravity at a Lifshitz Point

TL;DR

This paper reinterprets Horava gravity as a gauge-fixed, fully diffeomorphism-invariant theory with local anisotropy, propagating three degrees of freedom, and demonstrates consistent matter coupling.

Contribution

It extends Horava gravity to a fully invariant relativistic theory with local anisotropy and analyzes its degrees of freedom and matter coupling.

Findings

Propagates three degrees of freedom: two gravitons and one scalar.

Can be formulated as a gauge-fixed, fully invariant theory.

Matter can be consistently coupled to this gravity theory.

Abstract

We show that the Horava theory for the completion of General Relativity at UV scales can be interpreted as a gauge fixed theory, and it can be extended to an invariant theory under the full group of four-dimensional diffeomorphisms. In this respect, although being fully relativistic, it results to be locally anisotropic in the time-like and space-like directions defined by a family of irrotational observers. We show that this theory propagates generically three degrees of freedom: two of them are related to the four-dimensional diffeomorphism invariant graviton (the metric) and one is related to a propagating scalar mode. Finally, we note that in the present formulation, matter can be consistently coupled to gravity.