Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection

TL;DR

This paper develops a loop quantum cosmology quantization for homogeneous models with intrinsic curvature, ensuring stability and classical behavior at large volumes, and applies it to the Bianchi IX model near singularities.

Contribution

It introduces a new quantization approach for curved homogeneous models in loop quantum cosmology based on stability and continuum criteria.

Findings

Achieves a stable, non-singular evolution in the model.

Ensures compatibility with classical behavior at large volumes.

Provides insights into Bianchi IX dynamics near singularities.

Abstract

Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced by two criteria for an acceptable quantization, admissibility of a continuum approximation and local stability. A quantization of the corresponding Hamiltonian constraints is presented and shown to lead to a locally stable, non-singular evolution compatible with almost classical behavior at large volume. As an application, the Bianchi IX model and its modified behavior close to its classical singularity is explored.