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