Cosmological perturbations in the projectable version of Horava-Lifshitz gravity

We consider linear perturbations about a homogeneous and isotropic cosmological background in the projectable version of Horava-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 and is either ghost-like or tachyonic depending on the value of a free parameter. This indicates a problem for the projectable version of Horava-Lifshitz gravity.