Gravity and Discrete Symmetry

TL;DR

This paper explores a novel approach to general relativity on a space-time combining a four-dimensional manifold with a two-point space, leading to a scalar-tensor theory potentially related to Jordan-Brans-Dicke gravity.

Contribution

It generalizes the concepts of frame and connection on discrete spaces and derives a scalar field coupled to Einstein gravity from a generalized torsion-free condition.

Findings

Derived an action of a scalar field coupled to Einstein gravity.

Connected the model to Jordan-Brans-Dicke theory.

Extended differential calculus to discrete group spaces.

Abstract

Using the differential calculus on discrete group, we study the general relativity in the space-time which is the product of a four dimensional manifold by a two-point space. We generalize the usual concept of frame and connection in our space-time, and from the generalized torsion free condition we obtain an action of a scalar field coupled to Einstein gravity, which may be related to the Jordan-Brans-Dicke theory.