Extending the redshift-distance relation in cosmological general relativity to higher redshifts

The redshift-distance modulus relation, the Hubble Diagram, derived from Cosmological General Relativity has been extended to arbitrarily large redshifts. Numerical methods were employed and a density function was found that results in a valid solution of the field equations at all redshifts. The extension has been compared to 302 type Ia supernova data as well as to 69 Gamma-ray burst data. The latter however do not truly represent a 'standard candle' as the derived distance moduli are not independent of the cosmology used. Nevertheless the analysis shows a good fit can be achieved without the need to assume the existence of dark matter. The Carmelian theory is also shown to describe a universe that is always spatially flat. This results from the underlying assumption of the energy density of a cosmological constant Omega(Lambda)=1, the result of vacuum energy. The curvature of the universe is described by a spacevelocity metric where the energy content of the curvature at any epoch is Omega(K) = Omega(Lambda)- Omega = 1 - Omega, where Omega is the matter density of the universe. Hence the total density is always Omega(K) + Omega = 1.