Bouncing loop quantum cosmology in Gauss-Bonnet gravity
Abstract
We develop an effective Gauss-Bonnet extension of loop quantum cosmology, by introducing holonomy corrections in modified $F(\mathcal{G})$ theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of loop quantum gravity theories, and we result in having leading order corrections to the classical $F(\mathcal{G})$ theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes it possible to find the loop quantum cosmology corrected $F(\mathcal{G})$ theory that can realize various cosmological scenarios. We exemplify our theoretical constructions by using bouncing cosmologies, and we investigate which loop quantum cosmology corrected Gauss-Bonnet modified gravities can successfully realize such cosmologies.