Paving the way for transitions --- a case for Weyl geometry

TL;DR

This paper explores how Weyl geometry generalizes Riemannian geometry and Einstein gravity, offering new insights into physics, cosmology, and the relationship between gravity and particle physics.

Contribution

It demonstrates the relevance of Weyl geometric gravity to fundamental physics, linking it to scalar-tensor theories, electroweak interactions, and cosmological models with a static spacetime.

Findings

Weyl geometry relates to Jordan-Brans-Dicke theory.

Weyl's scale gauge hypothesis gains support from scalar fields.

A static cosmological model with inherent redshift is proposed.

Abstract

This paper presents three aspects by which the Weyl geometric generalization of Riemannian geometry, and of Einstein gravity, sheds light on actual questions of physics and its philosophical reflection. After introducing the theory's principles, it explains how Weyl geometric gravity relates to Jordan-Brans-Dicke theory. We then discuss the link between gravity and the electroweak sector of elementary particle physics, as it looks from the Weyl geometric perspective. Weyl's hypothesis of a preferred scale gauge, setting Weyl scalar curvature to a constant, gets new support from the interplay of the gravitational scalar field and the electroweak one (the Higgs field). This has surprising consequences for cosmological models. In particular it leads to a static (Weyl geometric) spacetime with "inbuilt" cosmological redshift. This may be used for putting central features of the present cosmological model into a wider perspective.