On the consistency of the Horava Theory

TL;DR

This paper performs a Hamiltonian analysis of a simplified Horava Theory model, demonstrating its equivalence to general relativity under certain conditions, thereby supporting its theoretical consistency.

Contribution

It provides a Hamiltonian analysis showing the classical equivalence of a truncated Horava Theory model to general relativity, clarifying the role of constraints and gauge fixing.

Findings

The model is equivalent to general relativity in a specific gauge.

The arbitrary coupling constant lambda does not deviate from general relativity.

The role of a second-class constraint is clarified.

Abstract

With the goal of giving evidence for the theoretical consistency of the Horava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Horava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant lambda. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of lambda deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model.