Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature

We compile an updated list of 38 measurements of the Hubble parameter $H(z)$ between redshifts $0.07\le z\le 2.36$ 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, $z_{\mathrm{d}\mathrm{a}}$, from these $H(z)$ data. Within the error bars, the measured $z_{\mathrm{d}\mathrm{a}}$ 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 $z_{\rm da} = 0.72 \pm 0.05
(0.84 \pm 0.03)$for$H_0 = 68 \pm 2.8\ (73.24 \pm 1.74)$kms$^{-1}$Mpc$^{-1}$ and should provide a reasonably model-independent estimate of this cosmological parameter. The $H(z)$ data are consistent with the standard spatially-flat $\mathrm{\Lambda }$CDM cosmological model but do not rule out non-flat models or dynamical dark energy models.