On Geometrically Unified Fields and Universal Constants

TL;DR

This paper extends Einstein gravity using Cartan geometry, allowing torsion to have a separate coupling constant, potentially making torsion effects relevant beyond the Planck scale.

Contribution

It develops the most general Einstein-Cartan-Sciama-Kibble theory with independent torsion and metric couplings, exploring implications of torsion at larger scales.

Findings

Torsion may influence physics beyond the Planck scale.

The theory introduces a second coupling constant for torsion.

Potential new interactions induced by torsion are discussed.

Abstract

We consider the Cartan extension of Riemann geometry as the basis upon which to build the Sciama--Kibble completion of Einstein gravity, developing the most general theory in which torsion and metric have two independent coupling constants: the main problem of the ESK theory was that torsion, having the Newton constant, was negligible beyond the Planck scale, but in this $\mathrm{ESK}^{2}$ theory torsion, with its own coupling constant, may be relevant much further Planck scales; further consequences of these torsionally-induced interactions will eventually be discussed.