Effective f (R) actions for modified loop quantum cosmologies

Although General Relativity (GR) is an extremely successful theory, at least for weak gravitational fields, it breaks down at very high energies. For example, extrapolating the expansion of the Universe backwards in time yields an infinite energy density, which is referred to as the initial singularity problem. Quantum Gravity is expected to provide a solution to this open question. In fact, one alternative scenario to the Big Bang, that avoids the singularity, is offered by Loop Quantum Cosmology (LQC), which predicts that the Universe undergoes a collapse to an expansion through a bounce. In this work we use metric f(R) gravity to reproduce the modified Friedmann equations, which have been obtained in the context of modified loop quantum cosmologies (mLQC). Using a order reduction method, we obtain covariant effective actions that lead to a bounce, for specific models of mLQC, considering a massless scalar field.