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 not truly represent a `standard candle' as the derived distance modulii 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 \textit{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 $\Omega_K + \Omega = 1$