A critical analysis of the cosmological implementation of Loop Quantum Gravity

TL;DR

This paper critically examines the construction of Loop Quantum Cosmology from Loop Quantum Gravity, highlighting issues with symmetry preservation and proposing a new perspective on the fundamental graph structure influencing cosmological models.

Contribution

It offers a critical analysis of LQC derivation from LQG, emphasizing the importance of the underlying graph structure and proposing a new approach to quantum cosmology.

Findings

Identifies issues with SU(2) symmetry preservation in LQC

Proposes a fundamental graph approach to quantum cosmology

Suggests a different minimum scale than traditional LQC

Abstract

This papers offers a critical discussion on the procedure by which Loop Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (LQG) theory. Revising recent issues in preserving SU(2) symmetry when quantizing the isotropic Universe, we trace a new perspective in approaching the cosmological problem within quantum geometry. The cosmological sector of LQG is reviewed and a critical point of view on LQC is presented. It is outlined how a polymer-like scale for quantum cosmology can be predicted from a proper fundamental graph underlying the homogeneous and isotropic continuous picture. However, such a minimum scale does not coincide with the choice made in LQC. Finally, the perspectives towards a consistent cosmological LQG model based on such a graph structure are discussed.