A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

TL;DR

This paper investigates how geometric quantities like expansion rate and shear scalar can be used to resolve singularities in loop quantum cosmology, leading to unique, physically viable models with bounded quantities and consistent quantum corrections.

Contribution

It introduces a geometric perspective to singularity resolution in loop quantum cosmology, identifying unique regularizations that ensure bounded physical quantities and consistent quantum effects.

Findings

Expansion rate is bounded only in the improved quantization for flat models.

In Bianchi-I spacetimes, only one regularization yields bounded expansion and shear.

This unique regularization leads to quantum gravity corrections at a single, physically meaningful scale.

Abstract

We re-examine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.