Some implications of signature-change in cosmological models of loop quantum gravity

TL;DR

This paper discusses the implications of signature change in loop quantum gravity cosmological models, highlighting mathematical consistency locally but potential global issues in the underlying theory.

Contribution

It provides a conceptual analysis of signature change effects in loop quantum gravity using mixed-type PDEs, emphasizing local regularity and global challenges.

Findings

Signature change can occur at high density in loop quantum gravity models.

Effective equations are locally regular and reliable.

Global problems may exist in the semiclassical solutions of the theory.

Abstract

Signature change at high density has been obtained as a possible consequence of deformed space-time structures in models of loop quantum gravity. This article provides a conceptual discussion of implications for cosmological scenarios, based on an application of mathematical results for mixed-type partial differential equations (the Tricomi problem). While the effective equations from which signature change has been derived are shown to be locally regular and therefore reliable, the underlying theory of loop quantum gravity may face several global problems in its semiclassical solutions.