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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 $λ$, generalized recently by da Silva, where $λ$ describes the deviation of the theory in the infrared from general relativity that has $λ_{GR} = 1$. We find that a scalar field in the Minkowski background becomes strong coupling for processes with energy higher than $Λ_ω [\equiv (M_{pl}/c_1)^{3/2} M_{pl}|λ- 1|^{5/4}]$, where generically $c_1 \ll M_{pl}$. However, this problem can be cured by introducing a new energy scale $M_{*}$, so that $M_{*} < Λ_ω$, where $M_{*}$ denotes the suppression energy of high order derivative terms of the theory.