Brans-Dicke theory with the cosmological constant from M_4 x Z_2 geometry

TL;DR

This paper derives a Brans-Dicke theory with a cosmological constant from a geometric framework based on M_4 x Z_2, clarifying the geometric origins of curvature, torsion, and the cosmological term.

Contribution

It introduces a novel geometric approach to derive Brans-Dicke theory with a cosmological constant from M_4 x Z_2 geometry, linking discrete extra dimensions to scalar-tensor gravity.

Findings

Derived explicit form of the cosmological term in Brans-Dicke theory.

Clarified the geometric relationship between curvature and torsion in the model.

Connected discrete geometry with scalar-tensor gravitational theories.

Abstract

The theory on M_4 x Z_2 geometry is applied to the Einstein gravity to yield the Brans-Dicke theory on M_4 geometry. The geometrical meaning and the relation between the curvatures and the torsions are clarified. The cosmological constant is also introduced into the pure Einstein action on M_4 x Z_2 in order to determine the explicit form of the cosmological term in the Brans-Dicke theory on M_4 geometry.