On strong coupling in nonrelativistic general covariant theory of gravity

TL;DR

This paper investigates the strong coupling issue in a generalized nonrelativistic gravity theory and proposes a solution involving a new energy scale to suppress problematic high-energy interactions.

Contribution

It identifies the conditions under which strong coupling occurs in the Horava-Lifshitz gravity with arbitrary coupling constant and introduces a mechanism to resolve this problem using a new energy scale.

Findings

Scalar field becomes strongly coupled above a certain energy scale $\\Lambda_{\omega}$

Introducing a new suppression scale $M_{*}$ can cure the strong coupling problem

The solution depends on the relation between $M_{*}$ and $\Lambda_{\omega}$

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 $M_{*}$, so that $M_{*} < \Lambda_{\omega}$, where $M_{*}$ denotes the suppression energy of high order derivative terms of the theory.