Stability, ghost, and strong coupling in nonrelativistic general
  covariant theory of gravity with $\lambda \not=1$
  In this paper, we investigate three important issues: stability, ghost and
strong coupling, in the Horava-Melby-Thompson setup of the Horava-Lifshitz
theory with $\lambda \not= 1$, generalized recently by da Silva. We first
develop the general linear scalar perturbations of the
Friedmann-Robertson-Walker (FRW) universe with arbitrary spatial curvature, and
find that an immediate by-product of the setup is that, in all the inflationary
models described by a scalar field, the FRW universe is necessarily flat.
Applying them to the case of the Minkowski background, we find that it is
stable, and, similar to the case $\lambda = 1$, the spin-0 graviton is
eliminated. The vector perturbations vanish identically in the Minkowski
background. Thus, similar to general relativity, a free gravitational field in
this setup is completely described by a spin-2 massless graviton even with
$\lambda \not= 1$. We also study the ghost problem in the FRW background, and
find explicitly the ghost-free conditions. To study the strong coupling
problem, we consider two different kinds of spacetimes all with the presence of
matter, one is cosmological and the one is static. We find that the coupling
becomes strong for a process with energy higher than $M_{pl} |c_{\psi}|^{5/2}$
in the flat FRW background, and $M_{pl}|c_{\psi}|^{3}$ in a static weak
gravitational field, where $|c_{\psi}| \equiv |(1-\lambda)/(3 \lambda
-1)|^{1/2}$.
