Scalar graviton in the healthy extension of Ho\v{r}ava-Lifshitz theory

TL;DR

This paper analyzes the behavior of scalar gravitons in a specific modified gravity theory, showing their oscillatory damping on small scales and phase freezing on large scales in a de Sitter universe.

Contribution

It provides the first detailed analytical and numerical study of scalar graviton dynamics in the healthy extension of Hořava-Lifshitz gravity in a de Sitter background.

Findings

Non-zero modes oscillate with damping on sub-horizon scales.

On super-horizon scales, phases freeze and modes approach asymptotic values.

Zero mode initially decays exponentially then stabilizes.

Abstract

In this note we study the linear dynamics of scalar graviton in a de Sitter background in the infrared limit of the healthy extension of Ho\v{r}ava-Lifshitz gravity with the dynamical critical exponent $z=3$. Both our analytical and numerical results show that the non-zero Fourier modes of scalar graviton oscillate with an exponentially damping amplitude on the sub-horizon scale, while on the super-horizon scale, the phases are frozen and they approach to some asymptotic values. In addition, as the case of the non-zero modes on super-horizon scale, the zero mode also initially decays exponentially and then approaches to an asymptotic constant value.