General cosmography model with spatial curvature

Abstract

ABSTRACT We adopt a cosmographic approach in order to determine spatial curvature (i.e. ΩK), combining the latest release of cosmic chronometer (CC) data, the Pantheon sample of Type Ia supernovae observations and baryon acoustic oscillation measurements. We use the expanded transverse comoving distance DM($z$) as a basic function for deriving H($z$) and other cosmic distances. In this scenario, ΩK can be constrained only by CC data. To overcome the convergence issues at high-redshift domains, two methods are applied: the Padé approximants and the Taylor series in terms of the new redshift y = $z$/(1 + $z$). Adopting the Bayesian evidence, we find that there is positive evidence for the Padé approximant up to order (2,2) and weak evidence for the Taylor series up to third order against the ΛCDM + ΩK model. The constraint results show that a closed Universe is preferred by present observations under all the approximations used in this study. Also, the tension level of the Hubble constant H0 has less than 2σ significance between different approximations and the local distance ladder determination. For each assumed approximation, H0 is anticorrelated with ΩK and the sound horizon at the end of the radiation drag epoch, which indicates that the H0 tension problem can be slightly relaxed by introducing ΩK or any new physics that can reduce the sound horizon in the early Universe.