# Bouncing cosmology in $f(R,\mathcal{G})$ gravity by order reduction

## TL;DR

This paper explores bouncing universe solutions within $f(R,)$ gravity using an order reduction method, aligning these solutions with Loop Quantum Cosmology to address the initial singularity problem.

## Contribution

It introduces an order reduction technique to find bouncing solutions in $f(R,)$ gravity that are perturbatively close to General Relativity and selects models matching Loop Quantum Cosmology.

## Key findings

- Identifies covariant gravitational actions that produce bouncing solutions.
- Demonstrates the compatibility of these actions with Loop Quantum Cosmology.
- Provides a method to select viable $f(R,)$ models for bouncing cosmologies.

## Abstract

A bouncing universe is a viable candidate to solve the initial singularity problem. Here we consider bouncing solutions in the context of $f(R,\mathcal{G})$ gravity by using an order reduction technique which allows one to find solutions that are perturbatively close to General Relativity. This procedure also acts as a model selection approach. Indeed, several covariant gravitational actions leading to a bounce are directly selected by demanding that the Friedmann equation derived within such gravity theories coincides with the one emerging from Loop Quantum Cosmology.