The Hybrid Euclidean-Lorentzian Universe: Stability Considerations and the Point of Transition

TL;DR

This paper explores a hybrid universe model combining Euclidean and Lorentzian metrics, addressing stability and transition criteria, and proposing solutions to initial singularity and CMB homogeneity issues.

Contribution

It introduces stability considerations and a mathematical criterion for the Euclidean-Lorentzian transition in a hybrid universe model.

Findings

Proposes a stability framework for the hybrid universe model.

Suggests a mathematical criterion for the Euclidean to Lorentzian transition.

Addresses solutions to initial singularity and CMB homogeneity problems.

Abstract

The limited velocity implied by Lorentzian signature, prevents the universe to reach thermodynamic equilibrium implied by the CMB. Rapid expansion can occur by following Hawking and assuming a primordial Euclidean metric, in which case velocity is not limited and thermalization and rapid expansion are derived without the need to assume an ad-hoc field. Moreover, a mathematical model was given regarding the development of current Lorentzian spacetime from the early Euclidean space-time in which problems such as initial singularity and the homogeneity of the CMB are solved. However, stability properties of the hybrid model were not discussed yet, nor was a mathematical criterion for the transition between the Euclidean and Lorentzian era's defined, those will be discussed here to some extent.