Quantization Ambiguities in Isotropic Quantum Geometry

TL;DR

This paper investigates quantization ambiguities in isotropic quantum geometry, showing they do not impact the resolution of classical singularities in loop quantum cosmology and revealing significant effects from non-fundamental representations.

Contribution

It provides a detailed analysis of quantization ambiguities in isotropic models and their effects on singularity resolution and operator modifications.

Findings

Ambiguities do not affect the classical singularity resolution.

Using non-fundamental SU(2) representations causes significant macroscopic corrections.

Explicit operator spectra calculations demonstrate robustness of the singularity avoidance.

Abstract

Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner. It is shown that those ambiguities do not affect the fate of the classical singularity, demonstrating that the absence of a singularity in loop quantum cosmology is a robust implication of the general quantization scheme. The calculations also allow conclusions about modified operators in the full theory. In particular, using holonomies in a non-fundamental representation of SU(2) to quantize connection components turns out to lead to significant corrections to classical behavior at macroscopic volume for large values of the spin of the chosen representation.