  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.
