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

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.

54 pp, 2 figs. To appear in D. Lehmkuhl (ed.) "Towards a Theory of Spacetime Theories", Einstein Studies, Basel: Birkhaeuser), revised version June 2015

References in corpus (7)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Local Conformal Symmetry in Physics and Cosmology
• The Renormalization Group and Weyl-invariance
• From Brans-Dicke gravity to a geometrical scalar-tensor theory
• Stable cosmological models driven by a free quantum scalar field
• The roots of scalar-tensor theory: an approximate history
• Cosmic age problem revisited in the holographic dark energy model

Cited by in corpus (4)

• Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation
• Gauge Theory of Gravity and Spacetime
• The problem of space in the light of relativity: the views of H. Weyl and E. Cartan
• Clusters of galaxies in a Weyl geometric approach to gravity