Gravitational conformal invariance and coupling constants in Kaluza-Klein theory

TL;DR

This paper explores how conformal invariance in a 5D Kaluza-Klein framework is broken by a cosmological scale, leading to Einstein equations with a small cosmological constant and dual matter couplings.

Contribution

It introduces a generalized conformal invariance in 5D Kaluza-Klein theory and analyzes its breaking via a cosmological scale, connecting 4D and 5D gravitational dynamics.

Findings

Conformal invariance in 5D is broken by a cosmological scale R_0.

The model yields Einstein equations with a small cosmological constant.

A dual Einstein equation couples matter to higher-dimensional geometry.

Abstract

We introduce a generalized gravitational conformal invariance in the context of non-compactified 5D Kaluza-Klein theory. It is done by assuming the 4D metric to be dependent on the extra non-compactified dimension. It is then shown that the conformal invariance in 5D is broken by taking an absolute cosmological scale $R_0$ over which the 4D metric is assumed to be dependent weakly on the 5th dimension. This is equivalent to Deser's model for the breakdown of the conformal invariance in 4D by taking a constant cosmological mass term $\mu^2\sim R_0^{-2}$ in the theory. We set the scalar field to its background cosmological value leading to Einstein equation with the gravitational constant $G_N$ and a small cosmological constant. A dual Einstein equation is also introduced in which the matter is coupled to the higher dimensional geometry by the coupling $G_N^{-1}$. Relevant interpretations of the results are also discussed.