Noncommutativity in Effective Loop Quantum Cosmology

TL;DR

This paper develops a noncommutative extension of Loop Quantum Cosmology for open FLRW models, exploring how theta deformations affect key features and the scalar field energy density.

Contribution

It introduces a novel noncommutative framework in Loop Quantum Cosmology, analyzing effects of deformations in configuration and momentum sectors.

Findings

Noncommutativity preserves key LQC features for free scalar fields.

Scalar field energy density remains bounded with maximum similar to standard LQC.

Deformations show compatibility with existing LQC paradigms.

Abstract

We construct a noncommutative extension of the Loop Quantum Cosmology effective scheme for the open FLRW model with a free scalar field via a theta deformation. Firstly, a deformation is implemented in the configuration sector, among the holonomy variable and the matter degree of freedom. We show that this type of noncommutativity retain, to some degree, key features of the Loop Quantum Cosmology paradigm for a free field. Secondly, a deformation is implemented in the momentum sector, among the momentum associated to the holonomy variable and the momentum associated to the matter field. We show that in this latter case the scalar field energy density is bounded and has the same maximum as in standard Loop Quantum Cosmology, signaling a higher degree of compatibility.