Kaluza-Klein Theory with Torsion confined to the Extra-dimension

TL;DR

This paper explores a 5D Kaluza-Klein model with torsion confined to the extra dimension, showing that torsion can be expressed in terms of the metric and does not affect 4D geodesic motion, leading to cosmological implications.

Contribution

It introduces a constrained torsion framework in 5D Kaluza-Klein theory, linking torsion to the metric and analyzing its cosmological effects.

Findings

Torsion components are fully determined by the metric.

Ricci tensor matches torsion-free general relativity on 4D hypersurfaces.

Cosmic acceleration emerges from the modified Einstein equations.

Abstract

Here we consider a variant of the 5 dimensional Kaluza-Klein theory within the framework of Einstein-Cartan formalism that includes torsion. By imposing a set of constraints on torsion and Ricci rotation coefficients, we show that the torsion components are completely expressed in terms of the metric. Moreover, the Ricci tensor in 5D corresponds exactly to what one would obtain from torsion-free general relativity on a 4D hypersurface. The contributions of the scalar and vector fields of the standard K-K theory to the Ricci tensor and the affine connections are completely nullified by the contributions from torsion. As a consequence, geodesic motions do not distinguish the torsion free 4D space-time from a hypersurface of 5D space-time with torsion satisfying the constraints. Since torsion is not an independent dynamical variable in this formalism, the modified Einstein equations are different from those in the general Einstein-Cartan theory. This leads to important cosmological consequences such as the emergence of cosmic acceleration.