  The velocity of the Hubble expansion has been added to General Relativity by
Moshe Carmeli and this resulted in new equations of motion for the expanding
universe. For the first time the observational magnitude-redshift data derived
from the high-$z$ supernova teams has been analysed in the framework of the
Carmeli theory and the fit to that theory is achieved without the inclusion of
any dark matter. Best fits to the data yield an averaged matter density for the
universe at the present epoch $\Omega_{m} \approx 0.021$, which falls well
within the measured values of the baryonic matter density. And the best
estimate of $\Omega_{\Lambda} + \Omega_{m} \approx 1.021$ at the present epoch.
The analysis also clearly distinguishes that the Hubble expansion of the
universe is speed-limited.
