Pathological behaviour of the scalar graviton in Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper confirms that in Hořava-Lifshitz gravity, the scalar graviton exhibits ghost-like behavior and instabilities in the infrared limit, challenging the theory's consistency and predictability.

Contribution

It analyzes the ghost and instability issues of the scalar graviton in Hořava-Lifshitz gravity and discusses the implications for the theory's validity.

Findings

Scalar graviton becomes a ghost with positive sound speed squared.

Negative and very small sound speed squared is required to avoid ghosts.

Higher order interactions dominate near the GR limit, invalidating linear analysis.

Abstract

We confirm the recent claims that, in the infrared limit of Ho\v{r}ava-Lifshitz gravity, the scalar graviton becomes a ghost if the sound speed squared is positive on the flat de Sitter and Minkowski background. In order to avoid the ghost and tame the instability, the sound speed squared should be negative and very small, which means that the flow parameter $\lambda$ should be very close to its General Relativity (GR) value. We calculate the cubic interactions for the scalar graviton which are shown to have a similar structure with those of the curvature perturbation in k-inflation models. The higher order interactions become increasing important for a smaller sound speed squared, that is, when the theory approaches GR. This invalidates any linearized analysis and any predictability is lost in this limit as quantum corrections are not controllable. This pathological behaviour of the scalar graviton casts doubt on the validity of the projectable version of the theory.