Stability of spin-0 graviton and strong coupling in Horava-Lifshitz theory of gravity

TL;DR

This paper investigates the stability of scalar modes and the strong coupling problem in Horava-Lifshitz gravity, demonstrating stability in de Sitter space, potential cures for Minkowski instability, and the limitations of existing mechanisms.

Contribution

It provides a detailed analysis of scalar mode stability in de Sitter space and explores the effectiveness of different mechanisms to address strong coupling issues in Horava-Lifshitz gravity.

Findings

Scalar modes are stable in de Sitter background due to curvature effects and exponential expansion.

Instability in Minkowski space can be cured by adding mass to the spin-0 graviton.

The Blas-Pujolas-Sibiryakov mechanism cannot resolve strong coupling, but the Vainshtein mechanism might.

Abstract

In this paper, we consider two different issues, stability and strong coupling, raised lately in the newly-proposed Horava-Lifshitz (HL) theory of quantum gravity with projectability condition. We find that all the scalar modes are stable in the de Sitter background, due to two different kinds of effects, one from high-order derivatives of the spacetime curvature, and the other from the exponential expansion of the de Sitter space. Combining these effects properly, one can make the instability found in the Minkowski background never appear even for small-scale modes, provided that the IR limit is sufficiently closed to the relativistic fixed point. At the fixed point, all the modes become stabilized. We also show that the instability of Minkowski spacetime can be cured by introducing mass to the spin-0 graviton. The strong coupling problem is investigated following the effective field theory approach, and found that it cannot be cured by the Blas-Pujolas-Sibiryakov mechanism, initially designed for the case without projectability condition, but might be circumvented by the Vainshtein mechanism, due to the non-linear effects. In fact, we construct a class of exact solutions, and show explicitly that it reduces smoothly to the de Sitter spacetime in the relativistic limit.