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

We discuss three aspects by which the Weyl geometric generalization of Riemannian geometry and Einstein gravity can shed light on present questions of physics and the philosophy of physics. The generalization of geometry goes back to Weyl's proposal of 1918; its guiding idea is the invariance of geometry and physical fields under ``local'', i.e. point dependent scale transformations. The generalization of gravity we start from was proposed by Omote, Utiyama, Dirac and others in the 1970s. Recently it has been taken up in work exploring a bridge between the Higgs field of electroweak theory and cosmology/gravity and has thus gained new momentum. This paper introduces the basics of the theory and discusses how it 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. Interestingly 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 (Higgs) one. This has surprising consequences for cosmological models. In particular it naturally leads to considering a static (Weyl geometric) spacetime with ``inbuilt'' cosmological redshift and gives rise to a critical reconsideration of the present status of cosmological modelling