Loop quantum cosmology of Bianchi IX: Effective dynamics

TL;DR

This paper numerically analyzes the effective dynamics of Bianchi IX models in Loop Quantum Cosmology, revealing singularity resolution, classical limit recovery, and complex phase transitions including Bianchi I, II, and VII_0 behaviors.

Contribution

It introduces a detailed numerical study of Bianchi IX effective solutions, including new Bianchi VII_0 phases, and compares different effective theories within Loop Quantum Cosmology.

Findings

Both effective theories resolve the big bang singularity.

Effective solutions recover classical GR at large volumes.

Bianchi IX solutions exhibit Bianchi I, II, and VII_0 phases.

Abstract

We study numerically the solutions to the effective equations of Bianchi IX spacetimes within Loop Quantum Cosmology. We consider Bianchi IX models with and without inverse triad corrections whose matter content is a scalar field without mass. The solutions are classified using the classical observables. We show that both effective theories --with lapse N=V and N=1-- solve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the spatial compactness, there is an infinity number of bounces and recollapses. We study the limit of large volume and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k=0,1 FLRW as well as Bianchi I, II, and VII_0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII_0 phases, which had not been studied before, at the quantum nor effective level. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour.