# On Gauge Invariant Cosmological Perturbations in UV-modified Horava Gravity

## TL;DR

This paper analyzes gauge invariant cosmological perturbations in UV-modified Horava gravity, demonstrating the recovery of Einstein gravity in IR, deriving scale-invariant spectra in non-inflationary backgrounds, and highlighting differences in fluctuation propagation.

## Contribution

It provides a Hamiltonian reduction analysis showing no extra graviton modes and derives scale-invariant spectra without inflation in UV-modified Horava gravity.

## Key findings

- No extra graviton modes; Einstein gravity recovered in IR
- Scale-invariant power spectra in non-inflationary backgrounds
- Tensor and scalar fluctuations propagate differently in UV

## Abstract

We consider gauge invariant cosmological perturbations in UV-modified, z=3 Horava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. In order to exhibit its dynamical degrees of freedom, we consider the Hamiltonian reduction method and find that, by solving "all" the constraint equations, the degrees of freedom are the same as those of Einstein gravity: One scalar and two tensor (graviton) modes when a scalar matter field presents. However, we confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for "non"-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion history of Universe. This could provide a new framework for the Big Bang cosmology. Moreover, we find that "tensor and scalar fluctuations travel differently in UV, generally". We present also some clarifying remarks about confusing points in the literatures.