An Alternative Approach for General Covariant Horava-Lifshitz Gravity and Matter Coupling

TL;DR

This paper introduces a gauge-invariant method for coupling matter to a nonrelativistic gravity theory, extending previous work on Horava-Lifshitz gravity, and clarifies the role of the parameter lambda in eliminating the spin-0 graviton.

Contribution

It proposes a minimal, gauge-invariant prescription for matter coupling in extended gauge symmetry Horava-Lifshitz gravity, clarifying the role of lambda in graviton elimination.

Findings

The method reproduces previous results with extended gauge symmetry.

The extended gauge invariance does not fix lambda to 1.

The spin-0 graviton is eliminated for any lambda value.

Abstract

Recently, Horava and Melby-Thompson proposed in arXiv:1007.2410 a nonrelativistic gravity theory with extended gauge symmetry that is free of the spin-0 graviton. We propose a minimal substitution recipe to implement this extended gauge symmetry which reproduce the results obtained by them. Our prescription has the advantage of being manifestly gauge invariant and immediately generalizable to other fields, like matter. We briefly discuss the coupling of gravity with scalar and vector fields found by our method. We show also that the extended gauge invariance in gravity does not force the value of $\lambda$ to be $\lambda=1$ as originally claimed. However, the spin-0 graviton is eliminated even for general $\lambda$.