Cosmological perturbations and classical change of signature

TL;DR

This paper investigates how cosmological perturbations behave in a universe with changing spacetime signature, finding no regular solutions at the signature change surface and comparing classical results with quantum cosmology.

Contribution

It provides a classical analysis of perturbations in signature-changing cosmologies and highlights the absence of regular solutions at the transition surface, contrasting with quantum cosmology findings.

Findings

No regular solutions satisfy junction conditions at signature change

Classical perturbations cannot smoothly cross the signature change surface

Comparison with quantum cosmology reveals differences in transition behavior

Abstract

Cosmological perturbations on a manifold admitting signature change are studied. The background solution consists in a Friedmann-Lemaitre-Robertson- Walker (FLRW) Universe filled by a constant scalar field playing the role of a cosmological constant. It is shown that no regular solution exist satisfying the junction conditions at the surface of change. The comparison with similar studies in quantum cosmology is made.