Radio Galaxies and the Acceleration of the Universe Beyond a Redshift of One

Radio galaxies provide a means to determine the coordinate distance,the luminosity distance, the dimensionless luminosity distance, or the angular size distance to sources with redshifts as large as two. Dimensionless coodinate distances for 55 supernovae and 20 radio galaxies are presented and discussed here. The radio galaxy results are consistent with those obtained using supernovae, suggesting that neither method is plagued by unknown systematic errors. The acceleration parameter q(z) and the expansion rate H(z) or dimensionless expansion rate E(z) can be determined directly from the data without having to make assumptions regarding the nature or evolution of the dark energy.'' The expansion rate E(z) can be determined from the first derivative of the dimensionless coordinate distance, and the acceleration parameter can be determined from a combination of the first and second derivatives of the dimensionless coordinate distance. A model-independent determination of E(z) will allow the properties and redshift evolution of the dark energy’’ to be determined, and a model-independent determination of q(z) will allow the redshift at which the universe transitions from acceleration to deceleration to be determined directly. Determination of E(z) and q(z) may also elucidate possible systematic errors in the determinations of the dimensionless coordinate distances.