  Already the simplest examples of Weyl geometry, the static space-time models
of general relativity modified by an additional time-homogeneous Weylian length
connection lead to beautiful cosmological models (Weyl universes) . The
magnitude-redshift 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 (ex-ante) spacelike curvature of Weyl
universes. Quasar frequency data from the SDSS provide strong evidence of a
positive ex-ante curvature. Thus an Einstein-Weyl universe, i.e., an Einstein
universe endowed with a Weylian length connection, is in good agreement with
supernovae and quasar data.
  The relative mass-energy density with respect to the critical density of the
standard approach, and the relative contribution of the ``vacuum term'' are
time-independent in Weyl gauge. Thus the time-evolution 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 Einstein-Weyl universe agrees
with the results of multipole measurements of CMB anisotropies.
