Bouncing Cosmology in Fourth-Order Gravity

TL;DR

This paper explores bouncing cosmological solutions within fourth-order gravity theories, using an order reduction technique to find perturbatively close solutions to General Relativity that address the initial singularity problem.

Contribution

It introduces a method to derive covariant effective actions in fourth-order gravity that admit bouncing solutions, reducing the equations to second-order for tractability.

Findings

Found covariant effective actions with bouncing solutions.

Demonstrated perturbative solutions close to General Relativity.

Provided a framework for addressing the initial singularity in cosmology.

Abstract

The Big Bang initial singularity problem can be solved by means of bouncing solutions. In the context of extended theories of gravity, we will look for covariant effective actions whose field equations contain up to fourth-order derivatives of the metric tensor. In finding such bouncing solutions, we will make use of an order reduction technique based on a perturbative approach. Reducing the order of the field equations to second-order, we are able to find solutions which are perturbatively close to General Relativity. We will build the covariant effective actions of the resulting order reduced theories.