Pre-classical solutions of the vacuum Bianchi I loop quantum cosmology

TL;DR

This paper demonstrates the existence of pre-classical solutions in vacuum Bianchi I loop quantum cosmology, which avoid classical singularities and are crucial for understanding the semiclassical limit of quantum cosmological models.

Contribution

It provides the first explicit demonstration of pre-classical solutions in vacuum Bianchi I models within loop quantum cosmology, advancing the understanding of their semiclassical behavior.

Findings

Pre-classical solutions exist for the vacuum Bianchi I model.

All solutions avoid the classical singularity at zero volume.

The solutions meet the criteria for a viable semiclassical limit.

Abstract

Loop quantization of diagonalized Bianchi class A models, leads to a partial difference equation as the Hamiltonian constraint at the quantum level. A criterion for testing a viable semiclassical limit has been formulated in terms of existence of the so-called pre-classical solutions. We demonstrate the existence of pre-classical solutions of the quantum equation for the vacuum Bianchi I model. All these solutions avoid the classical singularity at vanishing volume.