Revisiting the Hubble Constant, Spatial Curvature, and Cosmography with Strongly Lensed Quasar and Hubble Parameter Observations

Abstract

Abstract It is well known that time delays due to strong lensing offer the opportunity of a one-step measurement of the Hubble constant H 0 that is independent of the cosmic distance ladder. In this paper, we go further and propose a cosmological model-independent approach to simultaneously determine the Hubble constant and cosmic curvature with measurements of the time delay due to strong lensing, without any prior assumptions regarding the content of the universe. The data we use comprise the recent compilation of six well studied strongly lensed quasars, while the cosmic chronometer data are utilized to reconstruct distances via cosmographic parameters. In the framework of third-order Taylor expansion and (2, 1) order Padé approximation for cosmographic analysis, our results provide model-independent estimations of the Hubble constant H 0 = 72.24 − 2.52 + 2.73 km s − 1 Mpc − 1 and H 0 = 72.45 − 2.02 + 1.95 km s − 1 Mpc − 1 , which are well consistent with that derived from the local distance ladder by the SH0ES collaboration. The measured cosmic curvature Ω k = 0.062 − 0.078 + 0.117 and Ω k = 0.069 − 0.103 + 0.116 shows that zero spatial curvature is supported by the current observations of time delays due to strong lensing and cosmic chronometers. Imposing the prior of spatial flatness leads to more precise (at 1.6% level) determinations of the Hubble constant H 0 = 70.47 − 1.15 + 1.14 km s − 1 Mpc − 1 and H 0 = 71.66 − 1.57 + 1.15 km s − 1 Mpc − 1 , values located between the results from Planck and the SH0ES collaboration. If a prior of local (SH0ES) H 0 measurement is adopted, the constraint on curvature parameter can be further improved to Ω k = 0.123 − 0.046 + 0.060 and Ω k = 0.101 − 0.072 + 0.090 , supporting no significant deviation from a flat universe. Finally, we also discuss the effectiveness of the Padé approximation in reconstructing the cosmic expansion history for redshifts up to z ∼ 2.3, considering its better performance in the Bayes information criterion.