Dynamical Determination of the Metric Signature in Spacetime of Nontrivial Topology

TL;DR

This paper explores how quantum fields can dynamically determine the spacetime signature, suggesting the early universe may have transitioned from a higher-dimensional Euclidean space to a Lorentzian one.

Contribution

It demonstrates that the Lorentzian signature can arise dynamically in spacetimes with nontrivial topology, particularly in five-dimensional models with small compact dimensions.

Findings

Lorentzian signature can be dynamically generated in 5D spacetime with small T^1

Dynamical origin of Lorentzian signature also possible in 4D with trivial topology

Early universe could have been a multidimensional Lorentzian spacetime

Abstract

The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom induced by quantum fields is considered for spacetimes with nontrivial topology of the kind ${\bf R}^{D-1} \times {\bf T}^1$, for varying $D$. It is shown that a dynamical origin for the Lorentzian signature is possible in the five-dimensional space ${\bf R}^4 \times {\bf T}^1$ with small torus radius (periodic boundary conditions), as well as in four-dimensional space with trivial topology. Hence, the possibility exists that the early universe might have been of the Kaluza-Klein type, \ie multidimensional and of Lorentzian signature.