Anomaly-free perturbations with inverse-volume and holonomy corrections in Loop Quantum Cosmology

TL;DR

This paper develops an anomaly-free framework for cosmological perturbations in Loop Quantum Cosmology by combining holonomy and inverse-volume corrections, extending previous models and deriving consistent equations of motion.

Contribution

It introduces a unified, anomaly-free approach incorporating both key quantum corrections in Loop Quantum Cosmology for the first time.

Findings

Anomaly-free solutions including both corrections are found.

New possibilities in the inverse-volume correction case are identified.

Derived equations of motion for perturbations with combined corrections.

Abstract

This article addresses the issue of the closure of the algebra of constraints for generic (cosmological) perturbations when taking into account simultaneously the two main corrections of effective loop quantum cosmology, namely the holonomy and the inverse-volume terms. Previous works on either the holonomy or the inverse volume case are reviewed and generalized. In the inverse-volume case, we point out new possibilities. An anomaly-free solution including both corrections is found for perturbations, and the corresponding equations of motion are derived.