Cosmological spacetimes balanced by a scale covariant scalar field

Understand

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.