Description of Supernova Data in Conformal Cosmology without Cosmological Constant

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 $z>1.7$.