Dynamical Scalar Degree of Freedom in Horava-Lifshitz Gravity

TL;DR

This paper studies linear cosmological perturbations in Hořava-Lifshitz gravity, revealing a new gauge-invariant scalar mode that can generate a scale-invariant power spectrum, with its dynamical nature depending on the infrared regime.

Contribution

It demonstrates the emergence of a new gauge-invariant scalar mode in Hořava-Lifshitz gravity and analyzes its behavior across different regimes.

Findings

A new gauge-invariant scalar mode appears in the perturbation spectrum.

The scalar mode can produce a scale-invariant power spectrum.

In the infrared limit with λ=1, the scalar mode becomes non-dynamical.

Abstract

We investigate the linear cosmological perturbations of Ho\v{r}ava-Lifshitz gravity in a FRW universe without any matter. Our results show that a new gauge invariant dynamical scalar mode emerges, due to the gauge transformation under the "foliation-preserving" diffeomorphism and "projectability condition", and it can produce a scale invariant power spectrum. In the infrared regime with $\lambda=1$, the dynamical scalar degree of freedom turns to be a non-dynamical one at the linear order level.