Signature change from Schutz's canonical quantum cosmology and its classical analogue

TL;DR

This paper investigates signature change phenomena in quantum cosmology models using Schutz's formalism, revealing classical analogues with repulsive fluids and demonstrating signature transitions through wave packet analysis.

Contribution

It introduces a quantum cosmological model with signature change using Schutz's formalism and establishes its classical analogue involving a repulsive fluid.

Findings

Wave packets show signature transitions from Euclidean to Lorentzian.

Classical analogue involves a perfect fluid with a repulsive component.

Solutions exhibit finite Euclidean regions transitioning to Lorentzian domains.

Abstract

We study the signature change in a perfect fluid Friedmann-Robertson-Walker quantum cosmological model. In this work the Schutz's variational formalism is applied to recover the notion of time. This gives rise to a Schrodinger-Wheeler-DeWitt equation with arbitrary ordering for the scale factor. We use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor which coincides with the ontological interpretation. We show that these solutions exhibit signature transitions from a finite Euclidean to a Lorentzian domain. Moreover, such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid is present.