Signature Change by GUP

TL;DR

This paper demonstrates that a continuous signature transition in cosmological models can occur with a simple setup involving a free massless scalar field, a cosmological constant, and GUP-induced noncommutativity, without complex potentials.

Contribution

It shows that GUP-induced noncommutative phase space allows signature change in simple cosmological models with minimal scalar fields, simplifying previous requirements.

Findings

Signature transition occurs with a free massless scalar field and cosmological constant.

Quantum cosmology solutions align well with classical paths.

GUP deformation facilitates signature change without complex potentials.

Abstract

We revisit the issue of continuous signature transition from Euclidean to Lorentzian metrics in a cosmological model described by FRW metric minimally coupled with a self interacting massive scalar field. Then, using a noncommutative phase space of dynamical variables deformed by Generalized Uncertainty Principle (GUP) we show that the signature transition occurs even for a model described by FRW metric minimally coupled with a free massless scalar field accompanied by a cosmological constant. This indicates that the continuous signature transition might have been easily occurred at early universe just by a free massless scalar field, a cosmological constant and a noncommutative phase space deformed by GUP, without resorting to a massive scalar field having an {\it ad hoc} complicate potential. We also study the quantum cosmology of the model and obtain a solution of Wheeler-DeWitt equation which shows a good correspondence with the classical path.