Alternative route towards the change of metric signature

TL;DR

This paper proposes an alternative approach to metric signature change in cosmology, where spatial eigenvalues change sign, potentially simplifying the connection with big bang models and analyzing the necessary junction conditions.

Contribution

It introduces a novel method for metric signature transition by changing spatial eigenvalues, offering a different perspective from traditional temporal signature change models.

Findings

Derived junction conditions for spatial eigenvalue signature change

Showed the Riemannian side becomes purely timelike in this model

Provided insights into cosmological implications of spatial signature change

Abstract

Beginning with Hartle and Hawking's no-boundary proposal, it has long been known that the pathology of a big bang singularity can be suppressed if a transition into Riemannian (Euclidean) metric signature (the usual singularity theorems become invalid in this region) occurs when we track back along cosmic time. A vital component of this type of models, that needs to be clarified, is the set of junction conditions at the boundary between the two signature regimes. In the traditional approach, the signature change occurs in the temporal sector through a switch of sign in the lapse-squared function. Motivated by more straightforward connections with the big bang cosmology, we explore here an alternative whereby the spatial metric eigenvalues change sign instead, so that the Riemannian side is purely timelike. We investigate the junction conditions required in this case.