We compile a list of 28 independent measurements of the Hubble parameter between redshifts 0.07 ≤ z ≤ 2.3 and use this to place constraints on model parameters of constant and time-evolving dark energy cosmologies. These H(z) measurements by themselves require a currently accelerating cosmological expansion at about, or better than, 3 σ confidence. The mean and standard deviation of the 6 best-fit model deceleration-acceleration transition redshifts (for the 3 cosmological models and 2 Hubble constant priors we consider) is z da = 0.74 ± 0.05, in good agreement with the recent Busca et al. (2012) determination of z da = 0.82 ± 0.08 based on 11 H(z) measurements between redshifts 0.2 ≤ z ≤ 2.3, almost entirely from BAO-like data.

We compile an updated list of 38 measurements of the Hubble parameter H(z) between redshifts 0.07z2.36 and use them to place constraints on model parameters of constant and time-varying dark energy cosmological models, both spatially flat and curved. We use five models to measure the redshift of the cosmological deceleration-acceleration transition, z da , from these H(z) data. Within the error bars, the measured z da are insensitive to the model used, depending only on the value assumed for the Hubble constant H 0 . The weighted mean of our measurements is z da =0.72±0.05 (0.84±0.03) for H 0 =68±2.8 (73.24±1.74) km sand should provide a reasonably model-independent estimate of this cosmological parameter. The H(z) data are consistent with the standard spatially flat ΛCDM cosmological model but do not rule out nonflat models or dynamical dark energy models.

We use 21 Hubble parameter versus redshift data points, from Simon et al. (2005), Gaztañaga et al. (2009), Stern et al. (2010), and Moresco et al. (2012a), to place constraints on model parameters of constant and time-evolving dark energy cosmologies. The inclusion of the 8 new Moresco et al. (2012a) measurements results in H(z) constraints more restrictive than those derived by Chen & Ratra (2011b). These constraints are now almost as restrictive as those that follow from current Type Ia supernova (SNIa) apparent magnitude versus redshift data (Suzuki et al. 2012), which now more carefully account for systematic uncertainties. This is a remarkable result. We emphasize however that SNIa data have been studied for a longer time than the H(z) data, possibly resulting in a better estimate of potential systematic errors in the SNIa case. A joint analysis of the H(z), baryon acoustic oscillation peak length scale, and SNIa data favors a spatially-flat cosmological model currently dominated by a time-independent cosmological constant but does not exclude slowly-evolving dark energy.

We examine the observational viability of a class of f (R) gravity cosmological models. Particular attention is devoted to constraints from the recent observational determination of the redshift of the cosmological deceleration-acceleration transition. Making use of the fact that the Ricci scalar is a function of redshift z in these models, R = R(z), and so is f (z), we use cosmography to relate a f (z) test function evaluated at higher z to late-time cosmographic bounds. First, we consider a model independent procedure to build up a numerical f (z) by requiring that at z = 0 the corresponding cosmological model reduces to standard ΛCDM. We then infer late-time observational constraints on f (z) in terms of bounds on the Taylor expansion cosmographic coefficients. In doing so we parameterize possible departures from the standard ΛCDM model in terms of a two-parameter logarithmic correction. The physical meaning of the two parameters is also discussed in terms of the post Newtonian approximation. Second, we provide numerical estimates of the cosmographic series terms by using Type Ia supernova apparent magnitude data and Hubble parameter measurements. Finally, we use these estimates to bound the two parameters of the logarithmic correction. We find that the deceleration parameter in our model changes sign at a redshift consistent with what is observed.

Abstract.We constrain two non-flat time-evolving dark energy cosmological models by using Hubble parameter data, Type Ia supernova apparent magnitude measurements, and baryonic acoustic oscillation peak length scale observations. The inclusion of space curvature as a free parameter in the analysis results in a significant broadening of the allowed range of values of the parameter that governs the time evolution of the dark energy density in these models. While consistent with the "standard" spatially-flat ΛCDM cosmological model, these data are also consistent with a range of mildly non-flat, slowly time-varying dark energy models. After marginalizing over all other parameters, these data require the averaged magnitude of the curvature density parameter |Ω k0 | 0.15 at 1σ confidence.