Inflation in general covariant Ho\v{r}ava-Lifshitz gravity without
  projectability
  In this paper, we study inflation in the general covariant
Ho\v{r}ava-Lifshitz gravity without the projectability condition. We write down
explicitly the equations of the linear scalar perturbations of the FRW universe
for a single scalar field without specifying to any gauge. Applying these
equations to a particular gauge, we are able to obtain a master equation of the
perturbations, in contrast to all the other versions of the theory without the
projectability condition. This is because in the current version of the theory
it has the same degree of freedom of general relativity. To calculate the power
spectrum and index, we first define the initial conditions as the ones that
minimize the energy of the ground state. Then, we obtain the full solutions of
the equation of motion, by using the WKB approximations. From these solutions,
we calculate the power spectrum and spectrum index of the comoving curvature
perturbations and find the corrections due to the high order spatial derivative
terms of the theory to those standard results obtained in general relativity.
Remarkably, partly of corrections are a direct consequence of the
non-projectability condition. It is also shown that the perturbations are still
of scale-invariance, and the results obtained in the general covariant
Ho\v{r}ava-Lifshitz gravity without the projectability condition are consistent
with all current cosmological observations.
