# Linear cosmological perturbations in almost scale-invariant fourth-order gravity

## TL;DR

This paper investigates a specific class of modified gravity theories involving Ricci and Gauss-Bonnet scalars, deriving first-order cosmological perturbation equations to understand their implications for cosmology.

## Contribution

It introduces and analyzes a novel almost scale-invariant gravity model with a specific $f(R,G)$ form, deriving Einstein-like equations for cosmological perturbations.

## Key findings

- Derived first-order perturbation equations in the new gravity model.
- Provided a framework for analyzing cosmological implications of the theory.
- Enhanced understanding of scale-invariant modified gravity effects.

## Abstract

We study a class of almost scale-invariant modified gravity theories, using a particular form of $f(R, G) = \alpha R^2 + \beta G \log G$ where $R$ and $G$ are the Ricci and Gauss-Bonnet scalars, respectively and $\alpha$, $\beta$ are arbitrary constants. We derive the Einstein-like field equations to first order in cosmological perturbation theory in longitudinal gauge.