Direct determinations of the redshift behavior of the pressure, energy density, and equation of state of the dark energy and the acceleration of the universe

One of the goals of current cosmological studies is the determination of the expansion and acceleration rates of the universe as functions of redshift, and the determination of the properties of the dark energy that can explain these observations. Here the expansion and acceleration rates are determined directly from the data, without the need for the specification of a theory of gravity, and without adopting an a priori parameterization of the form or redshift evolution of the dark energy. We use the latest set of distances to SN standard candles from Riess et al. (2004), supplemented by data on radio galaxy standard ruler sizes, as described by Daly & Djorgovski (2003, 2004). We find that the universe transitions from acceleration to deceleration at a redshift of Z_T ≈ 0.4, with the present value of q₀ = -0.35 ± 0.15. The standard "concordance model" with Ω₀= 0.3 and Λ = 0.7 provides a reasonably good fit to the dimensionless expansion rate as a function of redshift, though it fits the dimensionless acceleration rate as a function of redshift less well. The expansion and acceleration rates are then combined with a theory of gravity to determine the pressure, energy density, and equation of state of the dark energy as functions of redshift. Adopting General Relativity as the correct theory of gravity, the redshift trends for the pressure, energy density, and equation of state of the dark energy out to z ≃ 1 are determined, and are found to be generally consistent with the concordance model; they have zero redshift values of p₀ = -0.6 ± 0.15, f₀ = 0.62 ± 0.05, and w₀ = -0.9 ± 0.1.