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.

Strong gravitational lens systems with time delays between the multiple images allow measurements of time-delay distances, which are primarily sensitive to the Hubble constant that is key to probing dark energy, neutrino physics, and the spatial curvature of the Universe, as well as discovering new physics. We present H0LiCOW (H 0 Lenses in COSMOGRAIL's Wellspring), a program that aims to measure H 0 with < 3.5% uncertainty from five lens systems (B1608+656, RXJ1131−1231, HE 0435−1223, WFI2033−4723 and HE 1104−1805). We have been acquiring (1) time delays through COSMOGRAIL and Very Large Array monitoring, (2) high-resolution Hubble Space Telescope imaging for the lens mass modeling, (3) wide-field imaging and spectroscopy to characterize the lens environment, and (4) moderate-resolution spectroscopy to obtain the stellar velocity dispersion of the lenses for mass modeling. In cosmological models with one-parameter extension to flat ΛCDM, we expect to measure H 0 to < 3.5% in most models, spatial curvature Ω k to 0.004, w to 0.14, and the effective number of neutrino species to 0.2 (1σ uncertainties) when combined with current CMB experiments. These are, respectively, a factor of ∼ 15, ∼ 2, and ∼ 1.5 tighter than CMB alone. Our data set will further enable us to study the stellar initial mass function of the lens galaxies, and the co-evolution of supermassive black holes and their host galaxies. This program will provide a foundation for extracting cosmological distances from the hundreds of time-delay lenses that are expected to be discovered in current and future surveys.

We present a blind time-delay strong lensing (TDSL) cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 . We combine the relative time delay between the quasar images, Hubble Space Telescope imaging, the Keck stellar velocity dispersion of the lensing galaxy, and wide-field photometric and spectroscopic data of the field to constrain two angular diameter distance relations. The combined analysis is performed by forward modelling the individual data sets through a Bayesian hierarchical framework, and it is kept blind until the very end to prevent experimenter bias. After unblinding, the inferred distances imply a Hubble constant H 0 = 68.8 +5.4 −5.1 km s −1 Mpc −1 , assuming a flat Λ cold dark matter cosmology with uniform prior on Ω m in [0.05, 0.5]. The precision of our cosmographic measurement with the doubly imaged quasar SDSS 1206+4332 is comparable with those of quadruply imaged quasars and opens the path to perform on selected doubles the same analysis as anticipated for quads. Our analysis is based on a completely independent lensing code than our previous three H0LiCOW systems and the new measurement is fully consistent with those. We provide the analysis scripts paired with the publicly available software to facilitate independent analysis. The consistency between blind measurements with independent codes provides an important sanity check on lens modelling systematics. By combining the likelihoods of the four systems under the same prior, we obtain H 0 = 72.5 +2.1 −2.3 km s −1 Mpc −1 . This measurement is independent of the distance ladder and other cosmological probes.

No abstract

The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H0 = 73.3−1.8+1.7 km s−1 Mpc−1, describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H0. We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H0. Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H0 = 74.5−6.1+5.6 km s−1 Mpc−1. Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H0 = 67.4−3.2+4.1 km s−1 Mpc−1. This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H0. While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data.