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On the geometry of cosmological model building

Erhard Scholz
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Abstract

This article analyzes the present anomalies of cosmology from the point of view of integrable Weyl geometry. It uses P.A.M. Dirac's proposal for a weak extension of general relativity, with some small adaptations. Simple models with interesting geometrical and physical properties, not belonging to the Friedmann-Lema\^ıtre class, are studied in this frame. Those with positive spatial curvature (Einstein-Weyl universes) go well together with observed mass density $Ω_m$, CMB, supernovae Ia data, and quasar frequencies. They suggest a physical role for an equilibrium state of the Maxwell field proposed by I.E. Segal in the 1980s (Segal background) and for a time invariant balancing condition of vacuum energy density. The latter leads to a surprising agreement with the BF-theoretical calculation proposed by C. Castro (2002).

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Erhard Scholz. 2005-11-21. On the geometry of cosmological model building. https://arxiv.org/abs/gr-qc/0511113

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