Cosmological Perturbations in the Projectable Version of Horava-Lifshitz Gravity

TL;DR

This paper analyzes linear cosmological perturbations in the projectable Hořava-Lifshitz gravity, revealing that an extra scalar mode is dynamical and exhibits ghost or tachyonic instabilities depending on the parameter λ, indicating issues with the theory.

Contribution

It provides a detailed analysis of the dynamical behavior of scalar perturbations in the projectable Hořava-Lifshitz gravity, highlighting fundamental instabilities not present in the non-projectable version.

Findings

The extra scalar mode is dynamical at linear order.

The mode is ghost-like for 1/3 < λ < 1.

The mode is tachyonic for λ < 1/3 or λ > 1.

Abstract

We consider linear perturbations about a homogeneous and isotropic cosmological background in the projectable version of Ho\v{r}ava-Lifshitz gravity. Starting from the action for cosmological perturbations, we identify the canonically normalized fluctuation variables. We find that - in contrast to what happens in the non-projectable version of the theory - the extra scalar cosmological perturbation mode is already dynamical at the level of linear perturbations. For values of the parameter $\lambda$ in the range $1/3 < \lambda < 1$, the extra mode is ghost-like, for values $1 < \lambda$ and $\lambda < 1/3$ it is tachyonic. This indicates a problem for the projectable version of Ho\v{r}ava-Lifshitz gravity.