Covariant action for bouncing cosmologies in modified Gauss-Bonnet gravity

TL;DR

This paper explores bouncing cosmological solutions within a modified Gauss-Bonnet gravity framework, employing an order reduction technique to find solutions close to general relativity and constructing a covariant action for the reduced theory.

Contribution

It introduces an order reduction method for $R+f(G)$ gravity to find bouncing solutions and constructs the covariant action of the reduced theory.

Findings

Found bouncing solutions perturbatively close to general relativity.

Developed a covariant action for the order reduced $R+f(G)$ theory.

Demonstrated the viability of cyclic universe models in modified gravity.

Abstract

Cyclic universes with bouncing solutions are candidates for solving the big bang initial singularity problem. Here we seek bouncing solutions in a modified Gauss-Bonnet gravity theory, of the type $R+f(G)$, where $R$ is the Ricci scalar, $G$ is the Gauss-Bonnet term, and $f$ some function of it. In finding such a bouncing solution we resort to a technique that reduces the order of the differential equations of the $R+f(G)$ theory to second order equations. As general relativity is a theory whose equations are of second order, this order reduction technique enables one to find solutions which are perturbatively close to general relativity. We also build the covariant action of the order reduced theory.