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

TL;DR

This paper develops a model-independent cosmographic analysis using strong gravitational lensing distance ratios, Type Ia supernovae, and DESI-DR2 BAO to constrain the expansion history and spatial curvature without assuming a specific dynamical model. By expanding the cosmographic series to fourth order in the y-parameter and applying the distance sum rule, the authors simultaneously constrain $H_0$, $\Omega_{k0}$, $q_0$, $j_0$, and $s_0$, with a focus on the curvature parameter via an independent route. The inclusion of DESI-DR2 data substantially tightens the constraints, yielding results largely compatible with a flat $\Lambda$CDM universe and improving the precision on higher-order cosmographic parameters, especially $s_0$. This second and final paper in the series demonstrates the power of lensing distance ratios as a complementary, geometry-driven probe for late-time cosmology and sets the stage for future refinements with additional data and advanced lens models.

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, $Ω_{k0}$, 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 $Λ$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.

Figures (4)

• Figure 1: (a) Posterior contours for SGL+PentheonPlus and SGL+PentheonPlus+DESI-DR2 datasets; (b)–(c) corresponding correlation matrices for each dataset combination.
• Figure 2: (a) Posterior contours for SGL+Union3 and SGL+Union3+DESI-DR2 datasets; (b)–(c) corresponding correlation matrices for each dataset combination.
• Figure 3: (a) Posterior contours for SGL+DESY5 and SGL+DESY5+DESI-DR2 datasets; (b)–(c) corresponding correlation matrices for each dataset combination.
• Figure 4: Tension matrix displaying the deviation from the reference values ($\Omega_{k0}=0$, $q_0 = -0.55$, $j_0 = 1$, $s_0 = -0.35$) in units of $\sigma$ for various observational combinations. The results highlight how the inclusion of DESI-DR2 data systematically reduces deviations, especially for higher-order cosmographic parameters.