Hubble Parameter and Baryon Acoustic Oscillation Measurement Constraints on the Hubble Constant, the Deviation from the Spatially-Flat $\Lambda$cdm Model, The Deceleration-Acceleration Transition Redshift, and Spatial Curvature

We compile a complete collection of reliable Hubble parameter $H(z)$ data to redshift $z \leq 2.36$ and use them with the Gaussian Process method to determine continuous $H(z)$ functions for various data subsets. From these continuous $H(z)$'s, summarizing across the data subsets considered, we find $H_0\sim 67 \pm 4\,\rm km/s/Mpc$, more consistent with the recent lower values determined using a variety of techniques. In most data subsets, we see a cosmological deceleration-acceleration transition at 2$\sigma$ significance, with the data subsets transition redshifts varying over $0.33<z_{\rm da}<1.0$ at 1$\sigma$ significance. We find that the flat-$\Lambda$CDM model is consistent with the $H(z)$ data to a $z$ of 1.5 to 2.0, depending on data subset considered, with 2$\sigma$ deviations from flat-$\Lambda$CDM above this redshift range. Using the continuous $H(z)$ with baryon acoustic oscillation distance-redshift observations, we constrain the current spatial curvature density parameter to be $\Omega_{K0}=-0.03\pm0.21$, consistent with a flat universe, but the large error bar does not rule out small values of spatial curvature that are now under debate.