Bouncing Cosmology in Fourth-Order Gravity

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