On strong coupling in nonrelativistic general covariant theory of gravity

We study the strong coupling problem in the Horava-Melby-Thompson setup of the Horava-Lifshitz gravity with an arbitrary coupling constant $\lambda$, generalized recently by da Silva, where $\lambda$ describes the deviation of the theory in the infrared from general relativity that has ${\lambda }_{GR}=1$. We find that a scalar field in the Minkowski background becomes strong coupling for processes with energy higher than $\Lambda_{\omega} [\equiv (M_{pl}/c_1)^{3/2} M_{pl}|\lambda - 1|^{5/4}]$,wheregenerically$c_1 \ll M_{pl}$\mathrm{.}However,thisproblemcanbecuredbyintroducinganewenergyscale$M_{}$,sothat$M_{} < \Lambda_{\omega}$,where$M_{*}$ denotes the suppression energy of high order derivative terms of the theory.