Cosmological spacetimes balanced by a scale covariant scalar field

A scale invariant, Weyl geometric, Lagrangian approach to cosmology is explored, with a a scalar field phi of (scale) weight -1 as a crucial ingredient besides classical matter \cite{Tann:Diss,Drechsler:Higgs}. For a particularly simple class of Weyl geometric models (called {\em Einstein-Weyl universes}) the Klein-Gordon equation for phi is explicitly solvable. In this case the energy-stress tensor of the scalar field consists of a vacuum-like term Lambda g_{mu nu} with variable coefficient Lambda, depending on matter density and spacetime geometry, and of a dark matter like term. Under certain assumptions on parameter constellations, the energy-stress tensor of the phi-field keeps Einstein-Weyl universes in locally stable equilibrium. A short glance at observational data, in particular supernovae Ia (Riess ea 2007), shows interesting empirical properties of these models.Comment: 28 pages, 1 figure, accepted by Foundations of Physic

The unexpected resurgence of Weyl geometry in late 20-th century physics

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor theories of gravity, foundations of gravity, foundations of quantum mechanics, elementary particle physics, and cosmology. It seems that Weyl geometry continues to offer an open research potential for the foundations of physics even after the turn to the new millennium.Comment: Completely rewritten conference paper 'Beyond Einstein', Mainz Sep 2008. Preprint ELHC (Epistemology of the LHC) 2017-02, 92 pages, 1 figur