Loop quantum cosmology of Bianchi type IX models

TL;DR

This paper investigates the loop quantum cosmology of Bianchi type IX models, demonstrating singularity resolution and deriving effective equations that incorporate quantum geometry effects.

Contribution

It extends loop quantum cosmology techniques to Bianchi type IX models without new input, showing singularity resolution and formulating effective equations.

Findings

Big bang and big crunch singularities are resolved.

Effective equations include quantum geometry modifications.

Techniques from Bianchi I and II models are successfully applied.

Abstract

The loop quantum cosmology "improved dynamics" of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present the effective equations which provide modifications to the classical equations of motion due to quantum geometry effects.