Bounce Loop Quantum Cosmology Corrected Gauss-Bonnet Gravity

TL;DR

This paper extends Gauss-Bonnet gravity within Loop Quantum Cosmology by incorporating holonomy corrections, providing a framework to reconstruct quantum-corrected models that can realize various bouncing cosmological scenarios.

Contribution

It introduces a perturbative formalism for Loop Quantum Gravity corrections in $F( ext{G})$ theories and develops a reconstruction method for bouncing cosmologies.

Findings

Derived leading order quantum corrections to classical $F( ext{G})$ gravity.

Reconstructed $F( ext{G})$ models that realize exponential and power-law bounces.

Analyzed behavior of quantum-corrected models near the bouncing point.

Abstract

We develop a 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 possible to find the Loop Quantum Cosmology corrected $F(\mathcal{G})$ theory that can realize various cosmological scenarios. Specifically, we studied exponential and power-law bouncing cosmologies, emphasizing on the behavior near the bouncing point and in some cases, the behavior for all the values of the cosmic time is obtained. 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.