Cosmological spacetimes balanced by a scale covariant scalar field

Abstract

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.

28 pages, 1 figure, accepted by Foundations of Physics

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• Dirac-Born-Infeld-Einstein theory with Weyl invariance
• The unexpected resurgence of Weyl geometry in late 20-th century physics
• The Mannheim-Kazanas solution, the conformal geometrodynamics and the dark matter
• Metric Measure Space as a Framework for Gravitation