Propagations of massive graviton in the deformed Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper investigates how massive gravitons propagate in deformed Hořava-Lifshitz gravity with Lorentz-violating mass terms, revealing that vector and tensor modes gain mass while scalar modes remain unstable.

Contribution

It introduces Lorentz-violating mass terms into Hořava-Lifshitz gravity and analyzes their effects on different graviton modes, highlighting stability issues.

Findings

Vector and tensor modes are massive on Minkowski background.

Scalar mode remains ghost unstable despite mass addition.

Mass terms do not resolve scalar ghost instability.

Abstract

We study massive graviton propagations of scalar, vector, and tensor modes in the deformed Ho\v{r}ava-Lifshitz gravity by introducing Lorentz-violating mass term. It turns out that vector and tensor modes are massively propagating on the Minkowski spacetime background. However, adding the mass term does not cure a ghost instability in the Ho\v{r}ava scalar.