Scale covariant gravity and equilibrium cosmologies

Erhard Scholz

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arXiv · gr-qc/0703102

Scale covariant gravity and equilibrium cosmologies

Erhard Scholz

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Abstract

Causal structure, inertial path structure and compatibility with quantum mechanics demand no full Lorentz metric, but only an integrable Weyl geometry for space time (Ehlers/Pirani/Schild 1972, Audretsch e.a. 1984). A proposal of (Tann 1998,,Drechsler/Tann 1999) for a minimal coupling of the Hilbert-Einstein action to a scale covariant scalar vacuum field $ϕ$ (weight -1) plus (among others) a Klein-Gordon action term opens the access to a scale covariant formulation of gravity. The ensuing scale covariant K-G equation specifies a natural scale gauge vacuum gauge). Adding other natural assumptions for gauge conditions (in particular Newton gauge, with unchanging Newton constant) the chosen Ansatz leads to a class of Weyl geometric Robertson-Walker solutions of the Einstein equation, satisfying $a''a+a'^2= const$, analogous to the Friedmann-Lemaitre equation but with completely different dynamical properties ($a$ the warp function in Riemann gauge). The class has an asymptotically attracting 1-parameter subfamily of extremely simple space-time geometries with an isotropic Robertson-Walker fluid as source of the Einstein equation, discussed as Weyl universes elsewhere (Scholz 2005). Under the assumption of a heuristic gravitational self energy binding Ansatz for the fluid, equilibrium solutions arise, in stark contrast to classical (semi-Riemannian) cosmology. Weyl universes agree very well with a variety of empirical data from observational cosmology, in particular supernovae luminosities and quasar data.

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Erhard Scholz. 2007-03-20. Scale covariant gravity and equilibrium cosmologies. https://arxiv.org/abs/gr-qc/0703102

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