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ABSTRACT We compare predictions for galaxy–galaxy lensing profiles and clustering from the Henriques et al. public version of the Munich semi-analytical model (SAM) of galaxy formation and the IllustrisTNG suite, primarily TNG300, with observations from KiDS + GAMA and SDSS-DR7 using four different selection functions for the lenses (stellar mass, stellar mass and group membership, stellar mass and isolation criteria, and stellar mass and colour). We find that this version of the SAM does not agree well with the current data for stellar mass-only lenses with $M_\ast \gt 10^{11}\, \mathrm{ M}_\odot$. By decreasing the merger time for satellite galaxies as well as reducing the radio-mode active galactic nucleus accretion efficiency in the SAM, we obtain better agreement, both for the lensing and the clustering, at the high-mass end. We show that the new model is consistent with the signals for central galaxies presented in Velliscig et al. Turning to the hydrodynamical simulation, TNG300 produces good lensing predictions, both for stellar mass-only (χ2 = 1.81 compared to χ2 = 7.79 for the SAM) and locally brightest galaxy samples (χ2 = 3.80 compared to χ2 = 5.01). With added dust corrections to the colours it matches the SDSS clustering signal well for red low-mass galaxies. We find that both the SAMs and TNG300 predict $\sim 50\, {{\ \rm per\ cent}}$ excessive lensing signals for intermediate-mass red galaxies with 10.2 < log10M*[M⊙] < 11.2 at $r \approx 0.6\, h^{-1}\, \text{Mpc}$, which require further theoretical development. 

The local expansion rate of the Universe is parametrized by the Hubble constant, H 0 , the ratio between recession velocity and distance. Different techniques lead to inconsistent estimates of H 0 . Observations of Type Ia supernovae (SNe) can be used to measure H 0 , but this requires an external calibrator to convert relative distances to absolute ones. We use the angular diameter distance to strong gravitational lenses as a suitable calibrator, which is only weakly sensitive to cosmological assumptions. We determine the angular diameter distances to two gravitational lenses, 810 − 130 + 160 and 1230 − 150 + 180 megaparsec, at redshifts z = 0.295 and 0.6304. Using these absolute distances to calibrate 740 previously measured relative distances to SNe, we measure the Hubble constant to be H 0 = 82.4 − 8.3 + 8.4 kilometers per second per megaparsec. 

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. 

Abstract We present the lens mass model of the quadruply-imaged gravitationally lensed quasar WFI2033−4723, and perform a blind cosmographical analysis based on this system. Our analysis combines (1) time-delay measurements from 14 years of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution Hubble Space Telescope imaging, (3) a measurement of the velocity dispersion of the lens galaxy based on ESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopy characterizing the lens environment. We account for all known sources of systematics, including the influence of nearby perturbers and complex line-of-sight structure, as well as the parametrization of the light and mass profiles of the lensing galaxy. After unblinding, we determine the effective time-delay distance to be $4784_{-248}^{+399}~\mathrm{Mpc}$, an average precision of $6.6{{\ \rm per\ cent}}$. This translates to a Hubble constant $H_{0} = 71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$, assuming a flat ΛCDM cosmology with a uniform prior on Ωm in the range [0.05, 0.5]. This work is part of the H0 Lenses in COSMOGRAIL’s Wellspring (H0LiCOW) collaboration, and the full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper (H0LiCOW XIII). 

Abstract We present a measurement of the Hubble constant (H0) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat ΛCDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}~\mathrm{km~s^{-1}~Mpc^{-1}}$, a $2.4{{\ \rm per\ cent}}$ precision measurement, in agreement with local measurements of H0 from type Ia supernovae calibrated by the distance ladder, but in 3.1σ tension with Planck observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in 5.3σ tension with Planck CMB determinations of H0 in flat ΛCDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat ΛCDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from Planck, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with Planck. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our H0 inference to cosmological model assumptions. For six different cosmological models, our combined inference on H0 ranges from ∼73–78 km s−1 Mpc−1, which is consistent with the local distance ladder constraints. 

ABSTRACT We present the measurement of the Hubble constant, H0, with three strong gravitational lens systems. We describe a blind analysis of both PG 1115+080 and HE 0435−1223 as well as an extension of our previous analysis of RXJ 1131−1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP (Strong-lensing High Angular Resolution Programme) AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL-measured time delays in these systems to determine H0. We do both an AO-only and an AO + HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives $H_{0}=82.8^{+9.4}_{-8.3}~\rm km\, s^{-1}\, Mpc^{-1}$ for PG 1115+080, $H_{0}=70.1^{+5.3}_{-4.5}~\rm km\, s^{-1}\, Mpc^{-1}$ for HE 0435−1223, and $H_{0}=77.0^{+4.0}_{-4.6}~\rm km\, s^{-1}\, Mpc^{-1}$ for RXJ 1131−1231. The joint AO-only result for the three lenses is $H_{0}=75.6^{+3.2}_{-3.3}~\rm km\, s^{-1}\, Mpc^{-1}$. The joint result of the AO + HST analysis for the three lenses is $H_{0}=76.8^{+2.6}_{-2.6}~\rm km\, s^{-1}\, Mpc^{-1}$. All of these results assume a flat Λ cold dark matter cosmology with a uniform prior on Ωm in [0.05, 0.5] and H0 in [0, 150] $\rm km\, s^{-1}\, Mpc^{-1}$. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of H0. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper.