Joint Constraints on the Hubble Constant, Spatial Curvature, and Sound Horizon from the Late-time Universe with Cosmography

Abstract: In this paper, using the latest Pantheon+ sample of Type Ia supernovae (SNe Ia), Baryon Acoustic Oscillation (BAO) measurements, and observational Hubble data (OHD), we carry out a joint constraint on the Hubble constant $H_0$, the spatial curvature $\Omega_{\rm K}$, and the sound horizon at the end of drag epoch $r_{\rm d}$. To be model-independent, four cosmography models, i.e., the Taylor series in terms of redshift $y_1=z/(1+z)$, $y_2=\arctan(z)$, $y_3=\ln(1+z)$, and the Pad\'e approximants, are used without the assumption of flat Universe. The results show that the $H_0$ is anti-correlated with $\Omega_{\rm K}$ and $r_{\rm d}$, indicating smaller $\Omega_{\rm K}$ or $r_{\rm d}$ would be helpful in alleviating the Hubble tension. And the values of $H_0$ and $r_{\rm d}$ are consistent with the estimate derived from the Planck Cosmic Microwave Background (CMB) data based on the flat $\Lambda$CDM model, but $H_0$ is in 2.3$\sim$3.0$\sigma$ tension with that obtained by \cite{Riess2022} in all these cosmographic approaches. Meanwhile, a flat Universe is preferred by the present observations under all approximations except the third order of $y_1$ and $y_2$ of the Taylor series. Furthermore, according to the values of the Bayesian evidence, we found that the flat $\Lambda$CDM remains to be the most favored model by the joint datasets, and the Pad\'e approximant of order (2,2), the third order of $y_3$ and $y_1$ are the top three cosmographic expansions that fit the datasets best, while the Taylor series in terms of $y_2$ are essentially ruled out.