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

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 ${\mathrm{\Omega }}_{\mathrm{K}}$, and the sound horizon at the end of drag epoch $r_{\mathrm{d}}$. To be model-independent, four cosmography models, i.e., the Taylor series in terms of redshift $y_1=z\mathrm{/}(1+z)$, $y_2=\arctan (z)$, $y_3=\ln (1+z)$, and the Padé approximants, are used without the assumption of flat Universe. The results show that the $H_0$ is anti-correlated with ${\mathrm{\Omega }}_{\mathrm{K}}$ and $r_{\mathrm{d}}$, indicating smaller ${\mathrm{\Omega }}_{\mathrm{K}}$ or $r_{\mathrm{d}}$ would be helpful in alleviating the Hubble tension. And the values of $H_0$ and $r_{\mathrm{d}}$ are consistent with the estimate derived from the Planck Cosmic Microwave Background (CMB) data based on the flat $\mathrm{\Lambda }$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 $\mathrm{\Lambda }$CDM remains to be the most favored model by the joint datasets, and the Padé 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.