We study the strong coupling problem in the Horava-Melby-Thompson setup of the Horava-Lifshitz theory of 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 ${\lambda }_{\mathrm{GR}}=1$. We find that a scalar field in the Minkowski background becomes strongly coupled for processes with energy higher than ${\Lambda }_{\omega }[\equiv (M_{pl}/c_1{)}^{3/2}{M}_{pl}|\lambda -1{|}^{5/4}]$, where generically $c_1\ll M_{pl}$. However, this problem can be cured by introducing a new energy scale $M_{*}$, so that $M_{*}<{\Lambda }_{\omega }$, where $M_{*}$ denotes the suppression energy of high-order derivative terms of the theory.

• Received 12 June 2011

DOI:https://doi.org/10.1103/PhysRevD.84.044051