Implications of the gauge-fixing in Loop Quantum Cosmology

TL;DR

This paper examines how gauge-fixing choices in Loop Quantum Cosmology influence the mathematical structure and quantization process, emphasizing the discretization of geometric spectra and the implementation of homogeneity.

Contribution

It clarifies the relationship between reduced and unreduced variables and explores the impact of gauge-fixing on the holonomy-flux algebra and quantum states in LQC.

Findings

Holonomy-flux algebra matches LQG when edges align with simplicial vectors.

Discretization of the area spectrum is confirmed within the model.

Diffeomorphism generators implement homogeneity on quantum states.

Abstract

The restriction to invariant connections in a Friedmann-Robertson-Walker space-time is discussed via the analysis of the Dirac brackets associated with the corresponding gauge fixing. This analysis allows us to establish the proper correspondence between reduced and un-reduced variables. In this respect, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if edges are parallel to simplicial vectors and the quantization of the model is performed via standard techniques by restricting admissible paths. Within this scheme, the discretization of the area spectrum is emphasized. Then, the role of the diffeomorphisms generator in reduced phase-space is investigated and it is clarified how it implements homogeneity on quantum states, which are defined over cubical knots. Finally, the perspectives for a consistent dynamical treatment are discussed.