  We consider cosmological consequences of a conformal invariant formulation of
Einstein's General Relativity where instead of the scale factor of the spatial
metrics in the action functional a massless scalar (dilaton) field occurs which
scales all masses including the Planck mass. Instead of the expansion of the
universe we get the Hoyle-Narlikar type of mass evolution, where the
temperature history of the universe is replaced by the mass history. We show
that this conformal invariant cosmological model gives a satisfactory
description of the new supernova Ia data for the effective magnitude - redshift
relation without a cosmological constant and make a prediction for the
high-redshift behavior which deviates from that of standard cosmology for
$z>1.7$.
