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This work and its companion paper, Amon et al. (2021), present cosmic shear measurements and cosmological constraints from over 100 million source galaxies in the Dark Energy Survey (DES) Year 3 data. We constrain the lensing amplitude parameter $S_8\equiv\sigma_8\sqrt{\Omega_\textrm{m}/0.3}$ at the 3% level in $\Lambda$CDM: $S_8=0.759^{+0.025}_{-0.023}$ (68% CL). Our constraint is at the 2% level when using angular scale cuts that are optimized for the $\Lambda$CDM analysis: $S_8=0.772^{+0.018}_{-0.017}$ (68% CL). With cosmic shear alone, we find no statistically significant constraint on the dark energy equation-of-state parameter at our present statistical power. We carry out our analysis blind, and compare our measurement with constraints from two other contemporary weak-lensing experiments: the Kilo-Degree Survey (KiDS) and Hyper-Suprime Camera Subaru Strategic Program (HSC). We additionally quantify the agreement between our data and external constraints from the Cosmic Microwave Background (CMB). Our DES Y3 result under the assumption of $\Lambda$CDM is found to be in statistical agreement with Planck 2018, although favors a lower $S_8$ than the CMB-inferred value by $2.3\sigma$ (a $p$-value of 0.02). This paper explores the robustness of these cosmic shear results to modeling of intrinsic alignments, the matter power spectrum and baryonic physics. We additionally explore the statistical preference of our data for intrinsic alignment models of different complexity. The fiducial cosmic shear model is tested using synthetic data, and we report no biases greater than 0.3$\sigma$ in the plane of $S_8\times\Omega_\textrm{m}$ caused by uncertainties in the theoretical models., Comment: Minor modifications, results unchanged. Matches version published in PRD. DES Y3 cosmology data products in https://des.ncsa.illinois.edu/releases/y3a2

We describe redMaPPer, a new red-sequence cluster finder specifically designed to make optimal use of ongoing and near-future large photometric surveys. The algorithm has multiple attractive features: (1) It can iteratively self-train the red-sequence model based on minimal spectroscopic training sample, an important feature for high redshift surveys; (2) It can handle complex masks with varying depth; (3) It produces cluster-appropriate random points to enable large-scale structure studies; (4) All clusters are assigned a full redshift probability distribution P(z); (5) Similarly, clusters can have multiple candidate central galaxies, each with corresponding centering probabilities; (6) The algorithm is parallel and numerically efficient: it can run a Dark Energy Survey-like catalog in ~500 CPU hours; (7) The algorithm exhibits excellent photometric redshift performance, the richness estimates are tightly correlated with external mass proxies, and the completeness and purity of the corresponding catalogs is superb. We apply the redMaPPer algorithm to ~10,000 deg^2 of SDSS DR8 data, and present the resulting catalog of ~25,000 clusters over the redshift range 0.08

We present a new measurement of the scaling relation between X-ray luminosity and total mass for 17,000 galaxy clusters in the maxBCG cluster sample. Stacking sub-samples within fixed ranges of optical richness, N_200, we measure the mean 0.1-2.4 keV X-ray luminosity, , from the ROSAT All-Sky Survey. The mean mass, , is measured from weak gravitational lensing of SDSS background galaxies (Johnston et al. 2007). For 9 <= N_200 < 200, the data are well fit by a power-law, /10^42 h^-2 erg/s = (12.6+1.4-1.3 (stat) +/- 1.6 (sys)) (/10^14 h^-1 M_sun)^1.65+/-0.13. The slope agrees to within 10% with previous estimates based on X-ray selected catalogs, implying that the covariance in L_X and N_200 at fixed halo mass is not large. The luminosity intercent is 30%, or 2\sigma, lower than determined from the X-ray flux-limited sample of Reiprich & Bohringer (2002), assuming hydrostatic equilibrium. This difference could arise from a combination of Malmquist bias and/or systematic error in hydrostatic mass estimates, both of which are expected. The intercept agrees with that derived by Stanek et al. (2006) using a model for the statistical correspondence between clusters and halos in a WMAP3 cosmology with power spectrum normalization sigma_8 = 0.85. Similar exercises applied to future data sets will allow constraints on the covariance among optical and hot gas properties of clusters at fixed mass., Comment: 5 pages, 1 figure, MNRAS accepted

Determining the scaling relations between galaxy cluster observables requires large samples of uniformly observed clusters. We measure the mean X-ray luminosity--optical richness (L_X--N_200) relation for an approximately volume-limited sample of more than 17,000 optically-selected clusters from the maxBCG catalog spanning the redshift range 0.1

Gravitational lensing is a powerful tool for the study of the distribution of dark matter in the Universe. The cold-dark-matter model of the formation of large-scale structures predicts the existence of quasars gravitationally lensed by concentrations of dark matter so massive that the quasar images would be split by over 7 arcsec. Numerous searches for large-separation lensed quasars have, however, been unsuccessful. All of the roughly 70 lensed quasars known, including the first lensed quasar discovered, have smaller separations that can be explained in terms of galaxy-scale concentrations of baryonic matter. Although gravitationally lensed galaxies with large separations are known, quasars are more useful cosmological probes because of the simplicity of the resulting lens systems. Here we report the discovery of a lensed quasar, SDSS J1004+4112, which has a maximum separation between the components of 14.62 arcsec. Such a large separation means that the lensing object must be dominated by dark matter. Our results are fully consistent with theoretical expectations based on the cold-dark-matter model., Comment: 10 pages, 3 figures, to appear in the 18th&25th Dec issue of Nature (Letters to Nature)

We study the recently discovered gravitational lens SDSS J1004+4112, the first quasar lensed by a cluster of galaxies. It consists of four images with a maximum separation of 14.62''. The system has been confirmed as a lensed quasar at z=1.734 on the basis of deep imaging and spectroscopic follow-up observations. We present color-magnitude relations for galaxies near the lens plus spectroscopy of three central cluster members, which unambiguously confirm that a cluster at z=0.68 is responsible for the large image separation. We find a wide range of lens models consistent with the data, but they suggest four general conclusions: (1) the brightest cluster galaxy and the center of the cluster potential well appear to be offset by several kpc; (2) the cluster mass distribution must be elongated in the North--South direction, which is consistent with the observed distribution of cluster galaxies; (3) the inference of a large tidal shear (~0.2) suggests significant substructure in the cluster; and (4) enormous uncertainty in the predicted time delays between the images means that measuring the delays would greatly improve constraints on the models. We also compute the probability of such large separation lensing in the SDSS quasar sample, on the basis of the CDM model. The lack of large separation lenses in previous surveys and the discovery of one in SDSS together imply a mass fluctuation normalization \sigma_8=1.0^{+0.4}_{-0.2} (95% CL), if cluster dark matter halos have an inner slope -1.5. Shallower profiles would require higher values of \sigma_8. Although the statistical conclusion might be somewhat dependent on the degree of the complexity of the lens potential, the discovery is consistent with the predictions of the abundance of cluster-scale halos in the CDM scenario. (Abridged), Comment: 21 pages, 24 figures, 5 tables, accepted for publication in ApJ

We present galaxy-galaxy lensing measurements over scales 0.025 to 10 Mpc/h in the Sloan Digital Sky Survey. Using a flux-limited sample of 127,001 lens galaxies with spectroscopic redshifts and mean luminosity = L_* and 9,020,388 source galaxies with photometric redshifts, we invert the lensing signal to obtain the galaxy-mass correlation function xi_{gm}. We find xi_{gm} is consistent with a power-law, xi_{gm} = (r/r_0)^{-gamma}, with best-fit parameters gamma = 1.79 +/- 0.06 and r_0 = (5.4+/-0.7)(0.27/Omega_m)^{1/gamma} Mpc/h. At fixed separation, the ratio xi_{gg}/xi_{gm} = b/r where b is the bias and r is the correlation coefficient. Comparing to the galaxy auto-correlation function for a similarly selected sample of SDSS galaxies, we find that b/r is approximately scale independent over scales 0.2-6.7 Mpc/h, with mean = (1.3+/-0.2)(Omega_m/0.27). We also find no scale dependence in b/r for a volume limited sample of luminous galaxies (-23.0 < M_r < -21.5). The mean b/r for this sample is _{Vlim} = (2.0+/-0.7)(Omega_m/0.27). We split the lens galaxy sample into subsets based on luminosity, color, spectral type, and velocity dispersion, and see clear trends of the lensing signal with each of these parameters. The amplitude and logarithmic slope of xi_{gm} increases with galaxy luminosity. For high luminosities (L ~5 L_*), xi_{gm} deviates significantly from a power law. These trends with luminosity also appear in the subsample of red galaxies, which are more strongly clustered than blue galaxies., Comment: 20 pages, 21 figures, prepared with emulateapj, Accepted to AJ, corrected some major typos