Multiple measurements on the cosmic curvature using Gaussian process regression without calibration and a cosmological model

In this letter, we propose an improved cosmological model-independent method to measure cosmic curvature, combining the recent measurements of transverse and line-of-sight directions in the baryon acoustic oscillations (BAO) with cosmic chronometers (CC) datasets. Considering that the CC dataset is discrete and includes only 32 $H(z)$ measurements, we apply Gaussian process (GP) regression to fit the CC dataset and reconstruct them. Our methodology, which does not need the calibration or selection of any cosmological model, provide multiple measurements of spatial curvature ($\Omega_K$) at different redshifts (depending on the redshift coverage of BAO dataset). For combination of all BAO data, we find that the constraint result on cosmic curvature is $\Omega_K=-0.096^{+0.190}_{-0.195}$ with $1\sigma$ observational uncertainty. Although the measured $\Omega_K$ is in good agreement with zero cosmic curvature within 1$\sigma$ confidence level, our result revels the fact of a closed universe. More importantly, our results show that the obtained $\Omega_K$ measurements are almost unaffected by different priors of the Hubble constant. This could help solve the issue of the Hubble tension that may be caused by inconsistencies in the spatial curvature between the early and late universes.