Covariant action for bouncing cosmologies in modified Gauss-Bonnet gravity

Understand

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.