Considerations on the Graviton Excitation Modes of Horava-Lifshitz Gravity

TL;DR

This paper introduces a new projection operator method to analyze the unitarity and spectral properties of Horava-Lifshitz gravity, simplifying the study of its degrees of freedom and gauge structure.

Contribution

It develops an alternative, systematic approach using projection operators to handle non-relativistic gravity theories with anisotropic scaling, including parity-violating terms.

Findings

Successfully tests unitarity of a general Horava-Lifshitz gravity model

Determines the number of propagating degrees of freedom

Clarifies gauge symmetry structure in the model

Abstract

A new set of projection operators is constructed to suitably handle non-relativistic theories of gravity with anisotropic scaling, including the ones with parity-violating terms. This alternative procedure allows us to discuss unitarity and spectral properties for different formulations of the Horava-Lifshitz gravity. This task, that generally involves lengthy algebraic steps, becomes more systematic and greatly simplified in terms of the projectors we work out. Moreover, this procedure allows us to fix the number of propagating degrees of freedom and the structure of gauge symmetries is readily determined. In order to test the efficacy of the technique at hand, the unitarity and low-energy regime of a general Horava-Lifshitz Gravity model are investigated.