Non-Projectable Horava-Lifshitz Gravity without Unwanted Scalar Graviton

TL;DR

This paper proposes a method to eliminate the problematic scalar graviton in Horava-Lifshitz gravity by introducing additional constraints, analyzing both projectable and non-projectable versions through canonical methods.

Contribution

It introduces specific constraints to remove the scalar graviton in Horava-Lifshitz gravity and analyzes their effects on the theory's constraint structure.

Findings

Scalar graviton can be eliminated in non-projectable theory with certain coupling constants.

Projectable theory is free of scalar graviton regardless of coupling constants.

Constraint structure varies with coupling constants in both theories.

Abstract

We consider a way of eliminating the unwanted scalar graviton from Horava-Lifshitz gravity. That is achieved via introduction of certain additional constraints. We perform canonical analysis of both projectable and non-projectable versions of the theory. We obtain the structure of constraints in each case, and analyze its dependence on the values of the coupling constants involved in the additional constraints. In the non-projectable theory, the scalar graviton is absent when the coupling constants have certain values, while for other values the scalar graviton appears. The projectable theory is free from the scalar graviton regardless of the values of the coupling constants, even though the structure of constraints does depend on the value of a coupling constant.