Cosmological Perturbations in the Projectable Version of Horava-Lifshitz Gravity

Abstract

We consider linear perturbations about a homogeneous and isotropic cosmological background in the projectable version of Hořava-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 Hořava-Lifshitz gravity.

13 pages

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