A Model‐Independent Determination of the Expansion and Acceleration Rates of the Universe as a Function of Redshift and Constraints on Dark Energy

Determination of the expansion and acceleration history of the universe isone of the fundamental goals of cosmology. Detailed measurements of these ratesas a function of redshift can provide new physical insights into the nature andevolution of the dark energy, which apparently dominates the global dynamics ofthe universe at the present epoch. We present here dimensionless coordinatedistances y(z) to twenty radio galaxies reaching out to z of about 1.8, theredshift range currently not covered by Supernova standard candle observations.We develop a simple numerical method for a direct determination of theexpansion and acceleration rates, E(z) and q(z), from the data, which makes noassumptions about the underlying cosmological model or the equation of stateparameter w. This differential method is in contrast to the traditionalcosmological tests, where particular model equations are integrated and thencompared with the observations. The new model-independent method is applied tocurrently available Supernova data and the data on radio galaxies presentedhere. We derive the expansion rate of the universe as a function of redshift,E(z), and for the first time obtain a direct estimate of the acceleration rateof the universe as a function of redshift, q(z), in a way that is independentof assumptions regarding the dark energy and its redshift evolution. Thecurrent observations indicate that the universe transitions from accelerationto deceleration at a redshift greater than 0.3, with a best fit estimate ofabout 0.45; this transition redshift and our determinations of E(z) are broadlyin agreement with the currently popular Friedmann-Lemaitre cosmology with Omega= 0.3, and Lambda = 0.7, even though no model assumptions are made in derivingthe fits for E(z) and q(z).Comment: 30 pages, 9 figures, to appear in ApJ, v597, Nov. 1, 200