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 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.
