TDCOSMO 2025: Cosmological constraints from strong lensing time delays

TL;DR

This work presents cosmological constraints from eight strongly lensed quasars (the TDCOSMO-2025 sample) augmented by two external lens samples, using a hierarchical Bayesian framework to jointly infer $H_0$ and the population properties of deflectors. By replacing SDSS-based kinematics with high-SNR JWST, KCWI, and MUSE data and by refining the treatment of line-of-sight effects, light profiles, and orbital anisotropy, the analysis robustly breaks the mass-sheet degeneracy and achieves conservative but precise results. In flat $\\Lambda$CDM, the baseline result is $H_0=71.6^{+3.9}_{-3.3}$ km s$^{-1}$ Mpc$^{-1}$ (Pantheon+ prior on $\\Omega_m$), with higher values when external lens samples are included; combining with Pantheon+ or DES-SN5YR or DESI-BAO yields consistent $H_0$ constraints across multiple cosmologies. The results are in good agreement with other late-Universe probes and help illuminate the Hubble tension, showing that time-delay cosmography remains a powerful, largely independent cross-check of cosmological models and dark-energy physics.

Abstract

We present cosmological constraints from 8 strongly lensed quasars (hereafter, the TDCOSMO-2025 sample). Building on previous work, our analysis incorporated new deflector stellar velocity dispersions measured from spectra obtained with the James Webb Space Telescope (JWST), the Keck Telescopes, and the Very Large Telescope (VLT), utilizing improved methods. We used integrated JWST stellar kinematics for 5 lenses, VLT-MUSE for 2, and resolved kinematics from Keck and JWST for RXJ1131-1231. We also considered two samples of non-time-delay lenses: 11 from the Sloan Lens ACS (SLACS) sample with Keck-KCWI resolved kinematics; and 4 from the Strong Lenses in the Legacy Survey (SL2S) sample. We improved our analysis of line-of-sight effects, the surface brightness profile of the lens galaxies, and orbital anisotropy, and corrected for projection effects in the dynamics. Our uncertainties are maximally conservative by accounting for the mass-sheet degeneracy in the deflectors' mass density profiles. The analysis was blinded to prevent experimenter bias. Our primary result is based on the TDCOSMO-2025 sample, in combination with $Ω_{\rm m}$ constraints from the Pantheon+ Type Ia supernovae (SN) dataset. In the flat $Λ$ cold dark matter (CDM), we find $H_0=71.6^{+3.9}_{-3.3}$ km s$^{-1}$ Mpc$^{-1}$. The SLACS and SL2S samples are in excellent agreement with the TDCOSMO-2025 sample, improving the precision on $H_0$ in flat $Λ$CDM to 4.6%. Using the Dark Energy Survey SN Year-5 dataset (DES-SN5YR) or DESI-DR2 baryonic acoustic oscillations (BAO) likelihoods instead of Pantheon+ yields very similar results. We also present constraints in the open $Λ$CDM, $w$CDM, $w_0w_a$CDM, and $w_φ$CDM cosmologies. The TDCOSMO $H_0$ inference is robust and consistent across all presented cosmological models, and our cosmological constraints in them agree with those from the BAO and SN.

Figures (17)

• Figure 1: Montage of the eight lensed quasar systems in the TDCOSMO-2025 sample. In each panel, the white bar illustrates the 1 scale. The false-color images are made from two or three bands from the HST, Keck-NIRCam, and Chandra X-ray imaging, given their availability. The image for DES J0408$-$5354 is adapted from Shajib2019, HE 0435$-$1223, B1608$+$656, and WFI 2033$-$4723 from Suyu2017, PG 1115$+$080 and SDSS J1206$+$4332 from Wong2019, RX J1131$-$1231 from Shajib2024revie, and WGD 2038$-$4008 from Shajib2022.
• Figure 2: JWST-NIRSpec spectra and kinematic fits for RX J1131$-$1231. Top left: The six annuli (black contours), from which summed spectra are extracted, are illustrated on top of the NIRSpec white-light image. The regions around the satellite galaxy and the closest quasar image are excluded. The white bar represents 1$\arcsec$ scale, and the North and East directions are pointed with emerald and yellow arrows, respectively. Bottom left: The measured $v_{\mathrm{rms}}$ in the six annuli. The horizontal error bars show the annulus widths, and the vertical error bars show the combined statistical and systematic uncertainty for each measurement. The measured values have 0.66% covariance on average. Second and third columns: The six panels show the integrated spectra in each annulus (gray boxes) and the kinematic fit (red line). The height of the gray box represents the nominal uncertainty levels estimated by the JWST pipeline, and the size of the vertical error bars represents the total boosted uncertainty levels to achieve $\chi^2_{\rm red} = 1$ for each fit. The vertical orange lines mark the wavelengths of the Calcium triplet lines from the lens galaxy, and the vertical blue lines mark the wavelengths of the H$\alpha$, [N ii], and [S ii] lines from the quasar host galaxy.
• Figure 3: JWST-NIRSpec integrated spectra (gray bars) and kinematic fits (red lines) for five TDCOSMO-2025 lenses. The height of the gray boxes represents the nominal uncertainty levels estimated by the JWST pipeline, the size of the vertical error bars represents the total boosted uncertainty levels to achieve $\chi^2_{\rm red} = 1$, and the width of the boxes represents the wavelength-pixel size. The $x$-axis shows the lens rest-frame wavelength. The gray-shaded vertical bands were masked during the fits due to contamination by the lensed quasar features.
• Figure 4: Measured values of $v_{\rm rms}$ for RX J1131$-$1231 in radial annuli from the JWST NIRSpec (left-hand panel, the same ones shown in Fig. \ref{['fig:RXJspectra']}) and Keck KCWI (middle panel). Both of these measurements marginalize over the same choices of template libraries, namely the Indo-US and the XSL DR3, in addition to separate choice combinations for polynomial orders and fitted wavelength range. The arrows in these panels illustrate the size of the PSF FWHM for each case ($0\farcs15$ for JWST-NIRSpec and $0\farcs96$ for Keck-KCWI): the higher resolution of the JWST-NIRSpec data enabled the identification of the sharp rise of the velocity dispersion profile in the center. The right-hand panel illustrates the 1D surface brightness profile in optical (blue line) and in the IR (red line). The optical light profile was extracted from double Sérsic fitting by Shajib23 from a large cutout that encapsulates the full extent of the galaxy in the HST F814W imaging (which corresponds to a pivot wavelength of 6208 $\rm \AA$ in the lens rest-frame). The IR light profile was extracted from the double Sérsic light profile fitted as part of the lens modeling done with a 2D image obtained from the NIRSpec datacube by summing within the wavelength range 8700--8800 $\rm \AA$ in the lens rest-frame. The surface brightness profiles are normalized by the corresponding amplitudes at $R=1\farcs3$ (vertical dashed line). For kinematic modeling of the NIRSpec kinematics, we use a stitched light profile that transitions from the IR light profile at $R \leq 1\farcs3$ to the optical light profile shape at $R > 1\farcs3$.
• Figure 5: VLT-MUSE spectra and kinematics fits with pPXF for DES J0408$-$5354 (left-hand panel) and WGD 2038$-$4008 (right-hand panel). The gray rectangles illustrate the data with the height representing the 1$\sigma$ uncertainty and the width representing the wavelength-pixel size. The red line illustrates the best-fit model. The principal spectral features probing the kinematics are the Ca H & K absorption lines marked with vertical orange lines. The gray-shaded region on the left-hand panel represents the wavelength range excluded from the fit.