On strong coupling in nonrelativistic general covariant theory of gravity

Abstract

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 ${\Lambda }_{\omega }[\equiv (M_{pl}/c_1{)}^{3/2}{M}_{pl}|\lambda -1{|}^{5/4}]$, where generically $c_1\ll M_{pl}$. However, this problem can be cured by introducing a new energy scale $M_{\ast }$, so that $M_{\ast }<{\Lambda }_{\omega }$, where $M_{\ast }$ denotes the suppression energy of high order derivative terms of the theory.

Comments: Some typos are corrected & new references added. revtex4, one figure. To appear in Physical Review D