An outline of Weyl geometric models in cosmology
Abstract
Already the simplest examples of Weyl geometry, the static spacetime models of general relativity modified by an additional timehomogeneous Weylian length connection lead to beautiful cosmological models (Weyl universes) . The magnituderedshift relation of recent supernovae Ia measurements is in perfect agreement with the prediction of decrease of energy flux in the Weyl models. These data allow to estimate the (exante) spacelike curvature of Weyl universes. Quasar frequency data from the SDSS provide strong evidence of a positive exante curvature. Thus an EinsteinWeyl universe, i.e., an Einstein universe endowed with a Weylian length connection, is in good agreement with supernovae and quasar data. The relative massenergy density with respect to the critical density of the standard approach, and the relative contribution of the ``vacuum term'' are timeindependent in Weyl gauge. Thus the timeevolution anomaly of vacuum energy does not arise. The intervals given in the literature for the dynamically determined matter density parameter are consistent with other data in the Weyl geometric approach. An explanation of the cosmic microwave background by a maximal entropy state of the quantized Maxwell equation, according to a proposal by I.E. Segal for the conformal Einstein universe, translates directly to the Weyl approach. It leads to quantitative estimations for the temperature of the Planck radiation between 2 and 5.3 deg K. Moreover, the anisotropy angles, expected to arise in an EinsteinWeyl universe agrees with the results of multipole measurements of CMB anisotropies.
 Publication:

arXiv eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:astroph/0403446
 Bibcode:
 2004astro.ph..3446S
 Keywords:

 Astrophysics
 EPrint:
 16 pages, 3 figures, condensed version of a paper submitted to Annalen der Physik