The Value of the Cosmological Constant in a Unified Field Theory with Enlarged Transformation Group

TL;DR

This paper explores a unified field theory extending spacetime geometry with an enlarged transformation group, showing that the free-field solution's scalar curvature aligns with the cosmological constant's negative value, supporting the theory's unification claim.

Contribution

It introduces a geometrical extension of spacetime using the Conservation group and investigates the free-field solutions' scalar curvature, linking it to the cosmological constant.

Findings

Scalar curvature asymptotically matches negative cosmological constant value

Supports the unification of fields in the extended geometrical framework

Provides a potential geometric explanation for the cosmological constant

Abstract

The geometrical structure of a real four-dimensional space-time has been extended via the Conservation group with basic field variable being the orthonormal tetrad. Field equations were obtained from a variational principle which is invariant under the conservation group. Recently, symmetric solutions of the field equations have been developed. In this note, the free-field solution is investigated in terms of the value of the scalar curvature. The resulting asymptotic value is approximately the negative of the currently accepted value of $\Lambda$, i.e. $R\approx - 10^{-120}$. This may add further support to the conclusion that the theory developed by Pandres unifies the fields.