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 φ of (scale) weight −1 as a crucial ingredient besides classical matter (Tann 1998, Drechsler 1999). For a particularly simple class of Weyl geometric models (called Einstein-Weyl universes) the Klein-Gordon equation for φ is explicitly solvable. In this case the energy-stress tensor of the scalar field consists of a vacuum-like term Λgμν with variable coefficient Λ, 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 φ-field keeps Einstein-Weyl universes in locally stable equilibrium. A short glance at observational data, in particular supernovae Ia (Riess e.a. 2007), shows interesting empirical properties of these models.