A cosmographic analysis using DESI-DR2 and strong lensing: II. Distance Ratio measurements

Abstract

The distance ratios derived from strong lensing systems, combined with complementary cosmological observations, allow for the study of cosmic expansion and curvature without assuming a fixed background cosmological model. In this work, we perform an analysis of cosmic expansion using the latest Type Ia supernova samples, including PantheonPlus, Union3, and DES Y5, combined with baryon acoustic oscillation dataset from DESI DR2 and strong-lensing distance ratios. The cosmic expansion is carried out to fourth order in the variable $y = z/(1+z)$, which allows constraints on the present-day deceleration, jerk, and snap parameters $(q_0, j_0, s_0)$. The analysis utilizes the distance sum rule to provide an independent determination of the spatial curvature parameter $Ω_{k0}$ without assuming any specific cosmological dynamics. Our results from combining strong lensing distance ratios with each supernova dataset indicate that a flat Universe remains consistent at the 95\% confidence level, and the inclusion of DESI-DR2 measurements tightens the parameter intervals while preserving agreement with flat geometry at the 68\% confidence level, in line with standard cosmology. The inferred values of $q_0$ and $j_0$ are compatible with $Λ$CDM predictions for all dataset combinations. The constraints on $s_0$ remain weak, although modest improvement appears after DESI DR2 data are included. This work represents the second and final paper in the two-part cosmography study.