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

## TL;DR

This study uses model-independent methods combining HII galaxy data and cosmic chronometers to measure spatial curvature, providing insights into the Hubble tension and favoring the Planck H_0 value over local measurements.

## Contribution

It introduces a novel, model-independent approach to estimate spatial curvature using Gaussian Process reconstruction of HII galaxy data and cosmic chronometers, addressing the Hubble tension.

## Key findings

- Spatial flatness favors the Planck H_0 measurement.
- Local H_0 measurement is ruled out at ~3 sigma.
- The method constrains curvature without assuming a specific cosmological model.

## Abstract

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. These data therefore reveal that the condition of spatial flatness favours the {\it 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 $\sim 3\sigma$.