Using spatial curvature with HII galaxies and cosmic chronometers to explore the tension in $H_0$

Understand

We present a model-independent measurement of spatial curvature $\Omega_{k}$ in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe, based on observations of the Hubble parameter $H(z)$ using cosmic chronometers, and a Gaussian Process (GP) reconstruction of the HII galaxy Hubble diagram.

• We show that the imposition of spatial flatness (i.e., $\Omega_k=0$) easily distinguishes between the Hubble constant measured with {\it Planck} and that based on the local distance ladder.
• We find an optimized curvature parameter $\Omega_{k} = -0.120^{+0.168}_{-0.147}$ when using the former (i.e., $H_0=67.66\pm0.42 \, \mathrm{km}\,\mathrm{s}^{-1} \,\mathrm{Mpc}^{-1}$), and $\Omega_{k} = -0.298^{+0.122}_{-0.088}$ for the latter ($H_0=73.24\pm 1.74 \,\mathrm{km}\,\mathrm{s}^{-1} \,\mathrm{Mpc}^{-1}$).
• The quoted uncertainties are extracted by Monte Carlo sampling, taking into consideration the covariances between the function and its derivative reconstructed by GP.