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Context.Constraining the mass-sheet degeneracy (MSD) is crucial for improving the precision and accuracy of time-delay cosmography. Joint analyses based on lensing and stellar kinematics have been widely adopted to break the MSD. A three-dimensional (3D) mass and stellar tracer population is required to accurately interpret the kinematics data. Aims.Our forward-modeling procedure is aimed at evaluating the projection effects using strong lensing and kinematics observables and to determine an optimal model assumption for the stellar kinematics analysis leading to an unbiased interpretation of the MSD andH₀. Methods.We numerically simulated the projection and selection effects for both a triaxial early-type galaxy (ETG) sample from the TNG100 simulation and an axisymmetric sample that matches the properties of slow-rotator galaxies representative of the strong lens galaxy population. Using the axisymmetric sample, we generated mock kinematics observables with spherically aligned axisymmetric Jeans anisotropic modeling (JAM) and assessed the kinematic recovery under different model assumptions. Using the triaxial sample, we quantified the random uncertainty introduced by modeling triaxial galaxies with axisymmetric JAM. Results.We show that spherical JAM analysis of spatially unresolved kinematic data introduces a bias of up to 2–4% (depending on the intrinsic shape of the lens) in the inferred MSD. Our model largely corrects this bias, resulting in a residual random uncertainty in the range of 0–2.2% in the stellar velocity dispersion (0–4.4% inH₀), depending on the projected ellipticity and the anisotropy of the stellar orbits. This residual uncertainty can be further mitigated by the use of spatially resolved kinematic data, which constrain the intrinsic axis ratio. We also show that the random uncertainty in the kinematics recovery using axisymmetric JAM for axisymmetric galaxies is at the level of 0.24% in the velocity dispersion, and the uncertainty using axisymmetric JAM for triaxial galaxies is at the level of 0.17% in the velocity dispersion. 

Time-delay cosmography leverages strongly lensed quasars to measure the Universe’s current expansion rate,H₀, independently from other methods. The latest TDCOSMO milestone measurement primarily used quadruply lensed quasars for their mass profile constraints. However, doubly lensed quasars, being more abundant and offering precise time delays, could expand the sample by a factor of 5, significantly advancing towards a 1% precision measurement ofH₀. We present the first TDCOSMO analysis of a doubly imaged source, HE 1104−1805, including the measurement of the four necessary ingredients. First, by combining 17 years of data from the SMARTS, Euler, and WFI telescopes, we measured a time delay of 176.3^+11.4_−10.3days. Second, using MUSE data, we extracted stellar velocity dispersion measurements in three radial bins with 5% to 13% precision. Third, employing F160W HST imaging for lens modelling and marginalising over various modelling choices, we measured the Fermat potential difference between the images. Fourth, using wide-field imaging, we measured the convergence added by objects not included in the lens modelling. By combining these four ingredients, we measured the time delay distance and the angular diameter distance to the deflector, favouring a power-law mass model over a baryonic and dark matter composite model. The measurement was performed blindly to prevent experimenter bias and resulted in a Hubble constant ofH₀=^+5.8_−5.0×λ_intkm s⁻¹Mpc⁻¹, whereλ_intis the internal mass sheet degeneracy parameter. This is in agreement with the TDCOSMO-2025 milestone and its precision forλ_int = 1 is comparable to that obtained with the best-observed quadruply lensed quasars (4–6%). This work is a stepping stone towards a precise measurement ofH₀using a large sample of doubly lensed quasars, supplementing the current sample. The next TDCOSMO milestone paper will include this system in its hierarchical analysis, constrainingλ_intandH₀jointly with multiple lenses. 

We present cosmological constraints from eight 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 theJames WebbSpace Telescope (JWST), the Keck Telescopes, and the Very Large Telescope (VLT), utilizing improved methods. We used integrated JWST stellar kinematics for five lenses, VLT-MUSE for 2, and resolved kinematics from Keck and JWST for RX J1131−1231. We also considered two samples of non-time-delay lenses: 11 from the Sloan Lens ACS (SLACS) sample with Keck-KCWI resolved kinematics; and four 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_mconstraints from the Pantheon+ Type Ia supernovae (SN) dataset. In the flat Λ cold dark matter (CDM), we findH₀= 71.6^+3.9_−3.3km s⁻¹Mpc⁻¹. The SLACS and SL2S samples are in excellent agreement with the TDCOSMO-2025 sample, improving the precision onH₀in flat ΛCDM 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 ΛCDM,wCDM,w₀w_aCDM, andw_ϕCDM cosmologies. The TDCOSMOH₀inference is robust and consistent across all presented cosmological models, and our cosmological constraints in them agree with those from the BAO and SN. 

Time-delay cosmography is a powerful technique to constrain cosmological parameters, particularly the Hubble constant (H₀). The TDCOSMO Collaboration is performing an ongoing analysis of lensed quasars to constrain cosmology using this method. In this work, we obtain constraints from the lensed quasar WGD 2038−4008 using new time-delay measurements and previous mass models by TDCOSMO. This is the first TDCOSMO lens to incorporate multiple lens modeling codes and the full time-delay covariance matrix into the cosmological inference. The models are fixed before the time delay is measured, and the analysis is performed blinded with respect to the cosmological parameters to prevent unconscious experimenter bias. We obtainD_Δt = 1.68_−0.38^+0.40Gpc using two families of mass models, a power-law describing the total mass distribution, and a composite model of baryons and dark matter, although the composite model is disfavored due to kinematics constraints. In a flat ΛCDM cosmology, we constrain the Hubble constant to beH₀ = 65₋₁₄⁺²³km s⁻¹Mpc⁻¹. The dominant source of uncertainty comes from the time delays, due to the low variability of the quasar. Future long-term monitoring, especially in the era of theVera C. RubinObservatory’s Legacy Survey of Space and Time, could catch stronger quasar variability and further reduce the uncertainties. This system will be incorporated into an upcoming hierarchical analysis of the entire TDCOSMO sample, and improved time delays and spatially-resolved stellar kinematics could strengthen the constraints from this system in the future. 

Abstract A quadruply lensed source, J125856.3–031944, has been discovered using the DELVE survey and Wide-field Infrared Survey Explorer W1–W2 colors. Follow-up direct imaging carried out with the Magellan Baade 6.5 m telescope is analyzed, as is spectroscopy from the 2.5 m Nordic Optical Telescope. The lensed image configuration is kite-like, with the major axis of the lensing galaxy along the symmetry axis of the kite, and with the faintest image at its tail. Redward of 6000 Å, the tail image is strongly blended with the lensing galaxy. The Sloangdirect imaging carried out with Magellan permits deblending. As the lensed image configuration is nearly circular, simple models give high predicted magnifications for all four images. The source’s narrow emission lines at redshiftz= 2.225 and low intrinsic luminosity qualify it as a type 2 active galactic nucleus. The Magellan image shows a substantial residual that suggests a second lensing galaxy. 

Strong-lensing time delays enable the measurement of the Hubble constant ( H 0 ) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H 0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate H 0 , effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy D d  = 865 −81 +85 Mpc and the time-delay distance D Δt  = 2180 −271 +472 Mpc, giving H 0  = 77.1 −7.1 +7.3 km s −1 Mpc −1 – for a flat Λ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and line-of-sight effects, and those related to the mass–anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ( H 0  = 78.3 −3.3 +3.4 km s −1 Mpc −1 ) and for seven lenses ( H 0  = 74.2 −1.6 +1.6 km s −1 Mpc −1 ), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ( H 0  = 73.3 −5.8 +5.8 km s −1 Mpc −1 ). This agreement corroborates the methodology of time-delay cosmography. 

ABSTRACT One of the main challenges in using high-redshift active galactic nuclei (AGNs) to study the correlations between the mass of a supermassive black hole ($$\mathcal {M}_{\rm BH}$$) and the properties of its active host galaxy is instrumental resolution. Strong lensing magnification effectively increases instrumental resolution and thus helps to address this challenge. In this work, we study eight strongly lensed AGNs with deep Hubble Space Telescope imaging, using the lens modelling code lenstronomy to reconstruct the image of the source. Using the reconstructed brightness of the host galaxy, we infer the host galaxy stellar mass based on stellar population models. $$\mathcal {M}_{\rm BH}$$ are estimated from broad emission lines using standard methods. Our results are in good agreement with recent work based on non-lensed AGNs, demonstrating the potential of using strongly lensed AGNs to extend the study of the correlations to higher redshifts. At the moment, the sample size of lensed AGNs is small and thus they provide mostly a consistency check on systematic errors related to resolution for non-lensed AGNs. However, the number of known lensed AGNs is expected to increase dramatically in the next few years, through dedicated searches in ground- and space-based wide-field surveys, and they may become a key diagnostic of black holes and galaxy co-evolution. 

One of the main challenges in using high redshift active galactic nuclei to study the correlations between the mass of the supermassive Black Hole (MBH) and the properties of their active host galaxies is instrumental resolution. Strong lensing magnification effectively increases instrumental resolution and thus helps to address this challenge. In this work, we study eight strongly lensed active galactic nuclei (AGN) with deep Hubble Space Telescope imaging, using the lens modelling code Lenstronomy to reconstruct the image of the source. Using the reconstructed brightness of the host galaxy, we infer the host galaxy stellar mass based on stellar population models. MBH are estimated from broad emission lines using standard methods. Our results are in good agreement with recent work based on non-lensed AGN, providing additional evidence that the correlation evolves over cosmic time. At the moment, the sample size of lensed AGN is small and thus they provide mostly a consistency check on systematic errors related to resolution for the non-lensed AGN. However, the number of known lensed AGN is expected to increase dramatically in the next few years, through dedicated searches in ground and space based wide field surveys, and they may become a key diagnostic of black hole and galaxy co-evolution. 

Context. Persistent tension between low-redshift observations and the cosmic microwave background radiation (CMB), in terms of two fundamental distance scales set by the sound horizon r d and the Hubble constant H 0 , suggests new physics beyond the Standard Model, departures from concordance cosmology, or residual systematics. Aims. The role of different probe combinations must be assessed, as well as of different physical models that can alter the expansion history of the Universe and the inferred cosmological parameters. Methods. We examined recently updated distance calibrations from Cepheids, gravitational lensing time-delay observations, and the tip of the red giant branch. Calibrating the baryon acoustic oscillations and type Ia supernovae with combinations of the distance indicators, we obtained a joint and self-consistent measurement of H 0 and r d at low redshift, independent of cosmological models and CMB inference. In an attempt to alleviate the tension between late-time and CMB-based measurements, we considered four extensions of the standard ΛCDM model. Results. The sound horizon from our different measurements is r d  = (137 ± 3 stat.  ± 2 syst. ) Mpc based on absolute distance calibration from gravitational lensing and the cosmic distance ladder. Depending on the adopted distance indicators, the combined tension in H 0 and r d ranges between 2.3 and 5.1 σ , and it is independent of changes to the low-redshift expansion history. We find that modifications of ΛCDM that change the physics after recombination fail to provide a solution to the problem, for the reason that they only resolve the tension in H 0 , while the tension in r d remains unchanged. Pre-recombination extensions (with early dark energy or the effective number of neutrinos N eff  = 3.24 ± 0.16) are allowed by the data, unless the calibration from Cepheids is included. Conclusions. Results from time-delay lenses are consistent with those from distance-ladder calibrations and point to a discrepancy between absolute distance scales measured from the CMB (assuming the standard cosmological model) and late-time observations. New proposals to resolve this tension should be examined with respect to reconciling not only the Hubble constant but also the sound horizon derived from the CMB and other cosmological probes.