Constraining the ΛCDM and wCDM Models of the Universe using Gravitational Lensing

Abstract

We investigate late-time cosmology using a compiled sample of ≈85 galaxy-scale strong gravitational lenses,

exploiting the fact that lensing directly probes geometry through the distance ratio Dls/Ds while remaining

effectively independent of the Hubble constant H0. For each system we infer Dls/Ds from the observed

Einstein radius and stellar velocity dispersion under a standard, spherically symmetric mass description of

the lens galaxy. We then confront these measurements with the predictions of two dark-energy scenarios

in a spatially flat universe: ΛCDM (cosmological constant) and wCDM with a constant, yet free, equation-

of-state parameter w. The theoretical distance ratios are computed from the expansion history E(z) and

line-of-sight integrals between the lens and source redshifts.

Parameter estimation proceeds via a straightforward χ2 minimization built from per-lens uncertainties,

yielding (i) profiled one-dimensional likelihood curves for Ωm0 and w, and (ii) joint confidence contours

in the (Ωm0,w) plane. The resulting constraints demonstrate that strong lensing alone provides precise,

H0-independent information on the matter density and dark-energy phenomenology. In ΛCDM, the best-fit

matter density and its confidence interval are obtained from the profiled χ2 curve; in wCDM, the two-

parameter contours capture the expected degeneracy between Ωm0 and w while still delivering competitive

bounds on each.

Overall, our analysis shows that a uniform treatment of galaxy-scale lenses—linking well-measured imag-

ing and stellar kinematics to distance-ratio predictions—offers a clean and efficient route to cosmological

constraints. The framework is simple, reproducible, and readily extensible: it can incorporate alternative

lens models, larger samples, or be combined with complementary probes (e.g., supernovae, BAO, CMB) to

further sharpen constraints and test the robustness of the late-time expansion.