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, baryon acoustic oscillation measurements, and observational Hubble data, we carry out a joint constraint on the Hubble constant H 0, the spatial curvature omega K, and the sound horizon at the end of the drag epoch r d. To be model-independent, four cosmography models-i.e., the Taylor series in terms of redshift y 1 = z/(1 + z), y2=arctan(z) , y3=ln(1+z) , and the Pade approximants-are used without the assumption of a flat Universe. The results show that H 0 is anticorrelated with omega K and r d, indicating that smaller omega K or r d would be helpful in alleviating the Hubble tension. The values of H 0 and r d are consistent with the estimate derived from the Planck cosmic microwave background data based on the flat Lambda CDM model, but H 0 is in 2.3 similar to 3.0 sigma tension with that obtained by Riess et al. 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 data sets, and the Pade approximant of order (2,2), the third order of y 3 and y 1 are the top three cosmographic expansions that fit the data sets best, while the Taylor series in terms of y 2 are essentially ruled out.