On the emergence of the Lorentz signature in an expanding universe

TL;DR

This paper proposes a mechanism for the transition from Euclidean to Lorentzian geometry in an expanding universe, linking it to a global texture defect and a boundary dividing different regions, with implications for early universe phase transitions.

Contribution

It introduces a novel interpretation of the Euclidean-Lorentzian transition as a consequence of a global texture defect affecting the manifold's symmetry.

Findings

Boundary divides Euclidean and Lorentzian regions

Homogeneous matter/energy fields preserve signature change

Horizon properties resemble Big Bang phase transition

Abstract

A mechanism producing the transition from an Euclidean to a Loretzian manifold is described. A global Robertson-Walker symmetry is assumed from the large scale data of the visible universe. Allowing for the strain of the manifold as an additional field in the Lagrangian, we interpret the symmetry as a consequence of a global texture defect. The additional term gives rise to a boundary dividing the manifold into an Euclidean plus a Lorentzian region. It is also shown that the presence in the early epoch of homogeneous matter/energy fields preserves the horizon and the signature change across it. The horizon has properties much similar to the ones of the Big Bang of the Standard Model, including the need for a phase transition of the scalar field producing particles and fields as we know them now.