Consistent Horava gravity without extra modes and equivalent to general relativity at the linearized level

TL;DR

This paper presents a Horava gravity model with a consistent constraint structure that propagates only two physical degrees of freedom, matches linearized general relativity at low energies, and avoids extra modes and strong-coupling issues.

Contribution

It introduces a specific Horava gravity formulation with lambda=1/3, ensuring the absence of extra scalar modes and equivalence to linearized GR in the IR, with a consistent quantum constraint structure.

Findings

The theory propagates only two physical degrees of freedom.

It matches linearized general relativity at the IR limit.

No strong-coupling problem arises due to the absence of extra modes.

Abstract

We consider a Horava theory that has a consistent structure of constraints and propagates two physical degrees of freedom. The Lagrangian includes the terms of Blas, Pujolas and Sibiryakov. The theory can be obtained from the general Horava's formulation by setting lambda = 1/3. This value of lambda is protected in the quantum formulation of the theory by the presence of a constraint. The theory has two second-class constraints that are absent for other values of lambda. They remove the extra scalar mode. There is no strong-coupling problem in this theory since there is no extra mode. We perform explicit computations on a model that put together a z = 1 term and the IR effective action. We also show that the lowest-order perturbative version of the IR effective theory has a dynamics identical to the one of linearized general relativity. Therefore, this theory is smoothly recovered at the deepest IR without discontinuities in the physical degrees of freedom.