Loop quantum cosmology and the k = - 1 RW model

TL;DR

This paper successfully extends loop quantum cosmology to the negatively curved k=-1 RW model, demonstrating a bounce in the universe's evolution and analyzing the effects of inverse volume modifications.

Contribution

It overcomes technical challenges to quantize the k=-1 RW model and explores its dynamics, including bounce predictions and inverse volume effects.

Findings

A bounce occurs in the backward evolution for a massless scalar field.

The model predicts vacuum repulsion leading to a bounce at high curvature.

Inverse volume modifications depend on an introduced length scale.

Abstract

The loop quantization of the negatively curved k=-1 RW model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the k=0,+1 models in a natural fashion. We discuss the resulting dynamics and show that for a universe consisting of a massless scalar field, a bounce is predicted in the backward evolution in accordance with the results of the k=0,+1 models. We also show that the model predicts a vacuum repulsion in the high curvature regime that would lead to a bounce even for matter with vanishing energy density. We finally comment on the inverse volume modifications of loop quantum cosmology and show that, as in the k=0 model, the modifications depend sensitively on the introduction of a length scale which a priori is independent of the curvature scale or a matter energy scale.