General covariant Horava-Lifshitz gravity without projectability condition and its applications to cosmology

TL;DR

This paper develops an extended Horava-Lifshitz gravity theory without the projectability condition, eliminating problematic scalar modes, ensuring stability of scalar fields, and predicting a flat universe in cosmological applications.

Contribution

It introduces a new version of Horava-Lifshitz gravity with an added U(1) symmetry, removing scalar graviton issues and applying it to cosmology with specific flat universe predictions.

Findings

Scalar field is stable in UV and IR regimes

The theory predicts a necessarily flat FRW universe

Scalar, vector, and tensor perturbation equations are derived

Abstract

We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry $ {{Diff}}(M, {\cal{F}})$ to include a local U(1) symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a scalar field, we find that the scalar field is not only stable in both the ultraviolet (UV) and infrared (IR), but also free of the strong coupling problem, because of the presence of high-order spatial derivative terms of the scalar field. Furthermore, applying the theory to cosmology, we find that due to the additional U(1) symmetry, the Friedmann-Robertson-Walker (FRW) universe is necessarily flat. We also investigate the scalar, vector, and tensor perturbations of the flat FRW universe, and derive the general linearized field equations for each kind of the perturbations.