Direct Determination of the Kinematics of the Universe and Properties of the Dark Energy as Functions of Redshift

Understanding the nature of dark energy, which appears to drive the expansion of the universe, is one of the central problems of physical cosmology today. In an earlier paper we proposed a novel method to determine the expansion rate E(z) and the deceleration parameter q(z) in a largely model-independent way, directly from the data on coordinate distances y(z). Here we expand this methodology to include measurements of the pressure of dark energy p(z), its normalized energy density fraction f(z), and the equation-of-state parameter w(z). We then apply this methodology to a new, combined data set of distances to supernovae and radio galaxies. In evaluating E(z) and q(z), we make only the assumptions that the FRW metric applies and that the universe is spatially flat (an assumption strongly supported by modern cosmic microwave background radiation measurements). The determinations of E(z) and q(z) are independent of any theory of gravity. For evaluations of p(z), f(z), and w(z), a theory of gravity must be adopted, and general relativity is assumed here. No a priori assumptions regarding the properties or redshift evolution of the dark energy are needed. We obtain trends for y(z) and E(z) that are fully consistent with the standard Friedmann-Lemaître concordance cosmology with Ω_0 = 0.3 and Λ_0 = 0.7. The measured trend for q(z) deviates systematically from the predictions of this model on a ~1-2 σ level but may be consistent for smaller values of Λ_0. We confirm our previous result that the universe transitions from acceleration to deceleration at a redshift zT ≈ 0.4. The trends for p(z), f(z), and w(z) are consistent with being constant at least out to z ~ 0.3-0.5 and broadly consistent with being constant out to higher redshifts, but with large uncertainties. For the present values of these parameters we obtain E_0 = 0.97 ± 0.03, q_0 = -0.35 ± 0.15, p_0 = -0.6 ± 0.15, f_0 = -0.62 - (Ω_0 - 0.3) ± 0.05, and w_0 = -0.9 - ε(Ω_0 - 0.3) ± 0.1, where Ω_0 is the density parameter for nonrelativistic matter and ε ≈ 1.5 ± 0.1. We note that in the standard Friedmann-Lemaître models p_0 = -Λ_0, and thus we can measure the value of the cosmological constant directly and obtain results in agreement with other contemporary results