Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections

TL;DR

This paper investigates loop quantum cosmology of Bianchi IX models, incorporating inverse triad corrections, and demonstrates singularity resolution through different quantization approaches and effective equations.

Contribution

It introduces new methods for implementing inverse triad corrections in Bianchi IX models and analyzes their effects on singularity resolution and physical observables.

Findings

Singularity is formally resolved in all quantization schemes.

Effective equations relate Bianchi IX to isotropic $k$=1 model.

Different inverse triad correction implementations impact physical predictions.

Abstract

We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic $k$=1 model that, classically, is contained within the Bianchi IX model. We use geometrically defined scalar observables to explore the physical implications of each of these theories. This is the first part in a series of papers analyzing different aspects of the Bianchi IX model, with inverse corrections, within loop quantum cosmology.