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

TL;DR

This study uses strong lensing and supernova data to perform a model-independent cosmographic analysis, constraining universe geometry and dynamics, and confirming flatness within standard cosmology with improved precision.

Contribution

It introduces a fourth-order cosmographic series expansion combined with the distance sum rule to independently assess spatial curvature without assuming a specific model.

Findings

Supports a flat universe at 95% confidence level.

Consistent $q_0$ and $j_0$ with $ ext{Lambda}$CDM.

Improved constraints on $s_0$ with DESI-DR2 data.

Abstract

The distance ratio derived from strong gravitational lensing systems, combined with complementary cosmological observations, offers a model-independent means to investigate the geometry and dynamics of the universe. In this study, we carry out a cosmographic investigation using the latest compilations of Type Ia supernovae (PantheonPlus, DESY5, and Union3), baryon acoustic oscillation measurements from DESI-DR2, and updated strong lensing distance ratios. The cosmographic series is expanded to fourth order in the variable $y = z/(1+z)$ to constrain the deceleration, jerk, and snap parameters $(q_0,~j_0,~s_0)$. The analysis utilizes the distance sum rule (DSR) to provide an independent assessment of the spatial curvature parameter, $\Omega_{k0}$, without assuming a specific dynamical model. Our results based on SGL distance ratio measurements combined with individual supernova datasets suggest a mild preference for an open universe, though a flat universe is supported at the 95% confidence level. Further, the inclusion of DESI-DR2 data in each combination provides tighter constraints on the parameters and confirms flatness within the 68% confidence level as expected in standard cosmology. The results for $q_0$ and $j_0$ are consistent with $\Lambda$CDM predictions across datasets, while the constraint on $s_0$ remains limited but improves with the inclusion of DESI-DR2. This is the second and final paper in a two-part series.