Instabilities in numerical loop quantum cosmology

TL;DR

This paper analyzes the numerical stability of difference equations in loop quantum cosmology models, revealing the presence of instabilities through von Neumann analysis and explicit wave-packet evolutions.

Contribution

It provides a systematic von Neumann stability analysis of loop quantum cosmology models, highlighting the conditions leading to instabilities in these numerical schemes.

Findings

Instabilities exist in certain domains of the models.

Explicit wave-packet evolutions demonstrate these instabilities.

Stability depends on the specific model constraints.

Abstract

In this article we perform von Neumann analysis of the difference equations that arise as a result of loop quantum gravity being applied to models of cosmology and black holes. In particular, we study the numerical stability of Bianchi I LRS (symmetric and non-symmetric constraint) and Schwarzschild interior (symmetric constraint) models, and find that there exist domains over which there are instabilities, generically. We also present explicit evolutions of wave-packets in these models and clearly demonstrate the presence of these instabilities.