A complete analysis of linear cosmological perturbations in
  Ho\v{r}ava-Lifshitz gravity
  We investigate the linear cosmological perturbations in Ho\v{r}ava-Lifshitz
gravity with a scalar field. Starting from the most general expressions of the
metric perturbations as well as that of a canonical scalar field, we decompose
the scalar, vector and tensor parts of the perturbed action. By reducing the
Hamiltonian, we find that there are two independent degrees of freedom for the
tensor perturbations while none for the vector perturbations. For the scalar
perturbations, the remaining number of degrees of freedom, which are all gauge
invariant, depends on whether the projectable condition is applied or not. For
both cases, we lose the time reparametrization symmetry of any kind.
