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 .