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 lenses with measured time delays between the multiple images and models of the lens mass distribution allow a one-step determination of the time-delay distance, and thus a measure of cosmological parameters. We present a blind analysis of the gravitational lens RXJ1131−1231 incorporating (1) the newly measured time delays from COSMOGRAIL, the COSmological MOnitoring of GRAvItational Lenses, (2) archival Hubble Space Telescope imaging of the lens system, (3) a new velocity-dispersion measurement of the lens galaxy of 323 ± 20 km s −1 based on Keck spectroscopy, and (4) a characterization of the line-of-sight structures via observations of the lens' environment and ray tracing through the Millennium Simulation. Our blind analysis is designed to prevent experimenter bias. The joint analysis of the data sets allows a time-delay distance measurement to 6% precision that takes into account all known systematic uncertainties. Time-delay lenses constrain especially tightly the Hubble constant H 0 (5.7% and 4.0% respectively in wCDM and open ΛCDM) and curvature of the universe. The overall information content is similar to that of Baryon Acoustic Oscillation experiments. Thus, they complement well other cosmological probes, and provide an independent check of unknown systematics. Our measurement of the Hubble constant is completely independent of those based on the local distance ladder method, providing an important consistency check of the standard cosmological model and of general relativity.

Strong gravitational lens systems with measured time delays between the multiple images provide a method for measuring the "time-delay distance" to the lens, and thus the Hubble constant. We present a Bayesian analysis of the strong gravitational lens system B1608+656, incorporating (1) new, deep Hubble Space Telescope (HST) observations, (2) a new velocity-dispersion measurement of 260 ± 15 km s −1 for the primary lens galaxy, and(3) an updated study of the lens' environment. Our analysis of the HST images takes into account the extended source surface brightness, and the dust extinction and optical emission by the interacting lens galaxies. When modeling the stellar dynamics of the primary lens galaxy, the lensing effect, and the environment of the lens, we explicitly include the total mass distribution profile logarithmic slope γ and the external convergence κ ext ; we marginalize over these parameters, assigning well-motivated priors for them, and so turn the major systematic errors into statistical ones. The HST images provide one such prior, constraining the lens mass density profile logarithmic slope to be γ = 2.08 ± 0.03; a combination of numerical simulations and photometric observations of the B1608+656 field provides an estimate of the prior for κ ext : 0.10 +0.08 −0.05 . This latter distribution dominates the final uncertainty on H 0 . Fixing the cosmological parameters at Ω m = 0.3, Ω Λ = 0.7, and w = −1 in order to compare with previous work on this system, we find H 0 = 70.6 +3.1 −3.1 km s −1 Mpc −1 . The new data provide an increase in precision of more than a factor of 2, even including the marginalization over κ ext . Relaxing the prior probability density function for the cosmological parameters to that derived from the Wilkinson Microwave Anisotropy Probe (WMAP) five-year data set, we find that the B1608+656 data set breaks the degeneracy between Ω m and Ω Λ at w = −1 and constrains the curvature parameter to be −0.031 < Ω k < 0.009 (95% CL), a level of precision comparable to that afforded by the current Type Ia SNe sample. Asserting a flat spatial geometry, we find that, in combination with WMAP, H 0 = 69.7 +4.9 −5.0 km s −1 Mpc −1 and w = −0.94 +0.17 −0.19 (68% CL), suggesting that the observations of B1608+656 constrain w as tightly as the current Baryon Acoustic Oscillation data do.

We present a new measurement of the Hubble Constant H 0 and other cosmological parameters based on the joint analysis of three multiply-imaged quasar systems with measured gravitational time delays. First, we measure the time delay of HE 0435−1223 from 13-year light curves obtained as part of the COSMOGRAIL project. Companion papers detail the modeling of the main deflectors and line of sight effects, and how these data are combined to determine the time-delay distance of HE 0435−1223. Crucially, the measurements are carried out blindly with respect to cosmological parameters in order to avoid confirmation bias. We then combine the timedelay distance of HE 0435−1223 with previous measurements from systems B1608+656 and RXJ1131−1231 to create a Time Delay Strong Lensing probe (TDSL). In flat ΛCDM with free matter and energy density, we find H 0 = 71.9 +2.4 −3.0 km s −1 Mpc −1 and Ω Λ = 0.62 +0.24 −0.35 . This measurement is completely independent of, and in agreement with, the local distance ladder measurements of H 0 . We explore more general cosmological models combining TDSL with other probes, illustrating its power to break degeneracies inherent to other methods. The joint constraints from TDSL and Planck are H 0 = 69.2 +1.4 −2.2 km s −1 Mpc −1 , Ω Λ = 0.70 +0.01 −0.01 and Ω k = 0.003 +0.004 −0.006 in open ΛCDM and H 0 = 79.0 +4.4 −4.2 km s −1 Mpc −1 , Ω de = 0.77 +0.02 −0.03 and w = −1.38 +0.14 −0.16 in flat w CDM. In combination with Planck and Baryon Acoustic Oscillation data, when relaxing the constraints on the numbers of relativistic species we find N eff = 3.34 +0.21 −0.21 in N eff ΛCDM and when relaxing the total mass of neutrinos we find Σm ν ≤ 0.182 eV in m ν ΛCDM. Finally, in an open w CDM in combination with Planck and CMB lensing we find H 0 = 77.9 +5.0 −4.2 km s −1 Mpc −1 , Ω de = 0.77 +0.03 −0.03 , Ω k = −0.003 +0.004 −0.004 and w = −1.37 +0.18 −0.23 .

Context. Weak-lensing surveys need accurate theoretical predictions for interpretation of their results and cosmological-parameter estimation. Aims. We study the accuracy of various approximations to cosmic shear and weak galaxy-galaxy lensing and investigate effects of Born corrections and lens-lens coupling. Methods. We use ray-tracing through the Millennium Simulation, a large N-body simulation of cosmic structure formation, to calculate various cosmic-shear and galaxy-galaxy-lensing statistics. We compare the results from ray-tracing to semi-analytic predictions. Results. (i) We confirm that the first-order approximation (i.e. neglecting lensing effects beyond first order in density fluctuations) provides an excellent fit to cosmic-shear power spectra as long as the actual matter power spectrum is used as input. Common fitting formulae, however, strongly underestimate the cosmic-shear power spectra (by >30% on scales > 10 000). Halo models provide a better fit to cosmic shear-power spectra, but there are still noticeable deviations (∼10%). (ii) Cosmic-shear B-modes, which are induced by Born corrections and lens-lens coupling, are at least three orders of magnitude smaller than cosmic-shear E-modes. Semianalytic extensions to the first-order approximation predict the right order of magnitude for the B-mode. Compared to the ray-tracing results, however, the semi-analytic predictions may differ by a factor two on small scales and also show a different scale dependence. (iii) The first-order approximation may under-or overestimate the galaxy-galaxy-lensing shear signal by several percent due to the neglect of magnification bias, which may lead to a correlation between the shear and the observed number density of lenses. Conclusions. (i) Current semi-analytic models need to be improved in order to match the degree of statistical accuracy expected for future weak-lensing surveys. (ii) Shear B-modes induced by corrections to the first-order approximation are not important for future cosmic-shear surveys. (iii) Magnification bias can be important for galaxy-galaxy-lensing surveys.

We present a comprehensive analysis of weak gravitational lensing by large-scale structure in the Hubble Space Telescope Cosmic Evolution Survey (COSMOS), in which we combine space-based galaxy shape measurements with ground-based photometric redshifts to study the redshift dependence of the lensing signal and constrain cosmological parameters. After applying our weak lensingoptimized data reduction, principal-component interpolation for the spatially, and temporally varying ACS point-spread function, and improved modelling of charge-transfer inefficiency, we measured a lensing signal that is consistent with pure gravitational modes and no significant shape systematics. We carefully estimated the statistical uncertainty from simulated COSMOS-like fields obtained from ray-tracing through the Millennium Simulation, including the full non-Gaussian sampling variance. We tested our lensing pipeline on simulated space-based data, recalibrated non-linear power spectrum corrections using the ray-tracing analysis, employed photometric redshift information to reduce potential contamination by intrinsic galaxy alignments, and marginalized over systematic uncertainties. We find that the weak lensing signal scales with redshift as expected from general relativity for a concordance ΛCDM cosmology, including the full cross-correlations between different redshift bins. Assuming a flat ΛCDM cosmology, we measure σ 8 (Ω m /0.3) 0.51 = 0.75 ± 0.08 from lensing, in perfect agreement with WMAP-5, yielding joint constraints Ω m = 0.266 +0.025 −0.023 , σ 8 = 0.802 +0.028 −0.029 (all 68.3% conf.). Dropping the assumption of flatness and using priors from the HST Key Project and Big-Bang nucleosynthesis only, we find a negative deceleration parameter q 0 at 94.3% confidence from the tomographic lensing analysis, providing independent evidence of the accelerated expansion of the Universe. For a flat wCDM cosmology and prior w ∈ [−2, 0], we obtain w < −0.41 (90% conf.). Our dark energy constraints are still relatively weak solely due to the limited area of COSMOS. However, they provide an important demonstration of the usefulness of tomographic weak lensing measurements from space.

Under the assumption of a flat ΛCDM cosmology, recent data from the Planck satellite point toward a Hubble constant that is in tension with that measured by gravitational lens time delays and by the local distance ladder. Prosaically, this difference could arise from unknown systematic uncertainties in some of the measurements. More interestingly -if systematics were ruled out -resolving the tension would require a departure from the flat ΛCDM cosmology, introducing for example a modest amount of spatial curvature, or a non-trivial dark energy equation of state. To begin to address these issues, we present here an analysis of the gravitational lens RXJ1131−1231 that is improved in one particular regard: we examine the issue of systematic error introduced by an assumed lens model density profile. We use more flexible gravitational lens models with baryonic and dark matter components, and find that the exquisite Hubble Space Telescope image with thousands of intensity pixels in the Einstein ring and the stellar velocity dispersion of the lens contain sufficient information to constrain these more flexible models. The total uncertainty on the time-delay distance is 6.6% for a single system. We proceed to combine our improved time-delay distance measurements with the WMAP9 and Planck posteriors. In an open ΛCDM model, the data for RXJ1131−1231 in combination with Planck favor a flat universe with Ω k = 0.00 +0.01 −0.02 (68% CI). In a flat wCDM model, the combination of RXJ1131−1231 and Planck yields w = −1.52 +0.19 −0.20 (68% CI).

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.