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.
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