A characteristic signature of fourth order gravity

TL;DR

This paper derives the complete matter power spectrum for $R^n$ gravity from fourth order scalar perturbation equations, revealing a unique signature that can serve as a crucial test for this modified gravity theory on cosmological scales.

Contribution

It provides the first complete matter power spectrum for $R^n$ gravity derived from fourth order perturbation equations, identifying a distinctive signature.

Findings

Discovered a characteristic signature of fourth order gravity in the matter power spectrum.

First derivation of the complete matter power spectrum for $R^n$ gravity from scalar perturbations.

Provides a new observational test for fourth order gravity theories.

Abstract

We present for the first time the complete matter power spectrum for $R^n$ gravity which has been derived from the fourth order scalar perturbation equations. This leads to the discovery of a characteristic signature of fourth order gravity in the matter power spectrum, the details of which have not seen before in other studies in this area and therefore provides a crucial test for fourth order gravity on cosmological scales.