On signature transition in Robertson-Walker cosmologies

TL;DR

This paper investigates signature-changing solutions in Robertson-Walker cosmologies with a scalar field, identifying conditions under which Euclidean to Lorentzian transitions occur, including bounds on the cosmological constant and scalar field properties.

Contribution

It demonstrates the existence of signature-changing solutions in non-flat Robertson-Walker models and clarifies the conditions, such as scalar field mass and cosmological constant bounds, necessary for these solutions.

Findings

Existence of signature-changing solutions in non-flat models.

Upper bound on the cosmological constant for such solutions.

Signature change requires constant scale factor and scalar field near the hypersurface.

Abstract

We analyse a classical model of gravitation coupled to a self interacting scalar field. We show that, within the context of this model for Robertson-Walker cosmologies, there exist solutions in the spatially non-flat cases exhibiting transitions from a Euclidean to a Lorentzian spacetime. We then discuss the conditions under which these signature changing solutions to Einstein's field equations exist. In particular, we find that an upper bound for the cosmological constant exists and that close to the signature changing hypersurface, both the scale factor and the scalar field have to be constant. Moreover we find that the signature changing solutions do not exist when the scalar field is massless.