Effective $f(R)$ actions for modified Loop Quantum Cosmologies via order reduction

TL;DR

This paper derives covariant $f(R)$ gravity actions that replicate modified loop quantum cosmology dynamics, specifically the bounce scenario, using an order reduction method on the field equations with scalar matter.

Contribution

It introduces a method to obtain effective $f(R)$ actions that reproduce modified LQC Friedmann equations via order reduction, bridging quantum cosmology and classical modified gravity.

Findings

Successfully reproduces bounce behavior with $f(R)$ models

Provides covariant actions matching modified LQC dynamics

Demonstrates applicability to scalar field matter models

Abstract

General Relativity is an extremely successful theory, at least for weak gravitational fields, however, it breaks down at very high energies, such as in correspondence of the initial singularity. Quantum Gravity is expected to provide more physical insights concerning this open question. Indeed, one alternative scenario to the Big Bang, that manages to completely avoid 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. To achieve this, we apply an order reduction method to the $f(R)$ field equations, and obtain covariant effective actions that lead to a bounce, for specific models of modified LQC, considering matter as a scalar field.