Signature transition in Einstein-Cartan cosmology

TL;DR

This paper explores how Einstein-Cartan gravity with spin interactions allows for smooth signature changes in cosmological models, providing insights into the transition from Euclidean to Lorentzian spacetime.

Contribution

It demonstrates that spin-spin interactions in Einstein-Cartan theory enable signature change solutions with degenerate metrics in cosmology.

Findings

Signature changing solutions are possible due to spin interactions.

Degenerate metrics facilitate smooth Euclidean-Lorentzian transition.

Riemann-Cartan structure underpins the signature change mechanism.

Abstract

In the context of Einstein-Cartan theory of gravity, we consider a Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model with Weyssenhoff perfect fluid. We focus attention on those classical solutions that admit a degenerate metric in which the scale factor has smooth behavior in the transition from a Euclidean to a Lorentzian domain. It is shown that the spin-spin contact interaction enables one to obtain such a signature changing solutions due to the Riemann-Cartan ($U_4$) structure of space-time.