Using Spatial Curvature with H

We present a model-independent measurement of spatial curvature Ω_k in the Friedmann-Lemaitre-Robertson-Walker universe, based on observations of the Hubble parameter H(z) using cosmic chronometers, and a Gaussian process (GP) reconstruction of the H ii galaxy Hubble diagram. We show that the imposition of spatial flatness (i.e., Ω_k = 0) easily distinguishes between the Hubble constant measured with Planck and that based on the local distance ladder. We find an optimized curvature parameter ω_k = -0.120_-0.147 ^+0.168 when using the former (i.e., H₀ = 67.66 ± 0.42 km s^-1 Mpc^-1), and ω_k = -0.298_-0.088 ^+0.122 for the latter (H₀ = 73.24 ± 1.74 Km s^-1 Mpc^-1). The quoted uncertainties are extracted by Monte Carlo sampling, taking into consideration the covariances between the function and its derivative reconstructed by GP. These data therefore reveal that the condition of spatial flatness favors the Planck measurement, while ruling out the locally inferred Hubble constant as a true measure of the large-scale cosmic expansion rate at a confidence level of ∼3σ.