Several key relations are derived for Cosmological General Relativity which are used in standard observational cosmology .
These include the luminosity distance , angular size , surface brightness and matter density .
These relations are used to fit type Ia supernova ( SNe Ia ) data , giving consistent , well behaved fits over a broad range of redshift 0.1 < z < 2 .
The best fit to the data for the local density parameter is \Omega _ { m } = 0.0401 \pm 0.0199 .
Because \Omega _ { m } is within the baryonic budget there is no need for any dark matter to account for the SNe Ia redshift luminosity data .
From this local density it is determined that the redshift where the universe expansion transitions from deceleration to acceleration is z _ { t } = 1.095 { } ^ { +0.264 } _ { -0.155 } .
Because the fitted data covers the range of the predicted transition redshift z _ { t } , there is no need for any dark energy to account for the expansion rate transition .
We conclude that the expansion is now accelerating and that the transition from a closed to an open universe occurred about 8.54 { Gyr } ago .