We present a joint cosmological analysis of weak gravitational lensing observations from the Kilo-Degree Survey (KiDS-1000), with redshift-space galaxy clustering observations from the Baryon Oscillation Spectroscopic Survey (BOSS) and galaxy-galaxy lensing observations from the overlap between KiDS-1000, BOSS, and the spectroscopic 2-degree Field Lensing Survey. This combination of large-scale structure probes breaks the degeneracies between cosmological parameters for individual observables, resulting in a constraint on the structure growth parameter S8 = σ8√(Ωm/0.3) = 0.766−0.014+0.020, which has the same overall precision as that reported by the full-sky cosmic microwave background observations from Planck. The recovered S8 amplitude is low, however, by 8.3 ± 2.6% relative to Planck. This result builds from a series of KiDS-1000 analyses where we validate our methodology with variable depth mock galaxy surveys, our lensing calibration with image simulations and null-tests, and our optical-to-near-infrared redshift calibration with multi-band mock catalogues and a spectroscopic-photometric clustering analysis. The systematic uncertainties identified by these analyses are folded through as nuisance parameters in our cosmological analysis. Inspecting the offset between the marginalised posterior distributions, we find that the S8-difference with Planck is driven by a tension in the matter fluctuation amplitude parameter, σ8. We quantify the level of agreement between the cosmic microwave background and our large-scale structure constraints using a series of different metrics, finding differences with a significance ranging between ∼3σ, when considering the offset in S8, and ∼2σ, when considering the full multi-dimensional parameter space.

We present cosmological constraints from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000), which doubles the survey area with nine-band optical and near-infrared photometry with respect to previous KiDS analyses. Adopting a spatially flat standard cosmological model, we find S8 = σ8(Ωm/0.3)0.5 = 0.759−0.021+0.024 for our fiducial analysis, which is in 3σ tension with the prediction of the Planck Legacy analysis of the cosmic microwave background. We compare our fiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis with complementary analyses of the two-point shear correlation function and band power spectra, finding the results to be in excellent agreement. We investigate the sensitivity of all three statistics to a number of measurement, astrophysical, and modelling systematics, finding our S8 constraints to be robust and dominated by statistical errors. Our cosmological analysis of different divisions of the data passes the Bayesian internal consistency tests, with the exception of the second tomographic bin. As this bin encompasses low-redshift galaxies, carrying insignificant levels of cosmological information, we find that our results are unchanged by the inclusion or exclusion of this sample.

Context. The Kilo-Degree Survey (KiDS) is an ongoing optical wide-field imaging survey with the OmegaCAM camera at the VLT Survey Telescope, specifically designed for measuring weak gravitational lensing by galaxies and large-scale structure. When completed it will consist of 1350 square degrees imaged in four filters (ugri). Aims. Here we present the fourth public data release which more than doubles the area of sky covered by data release 3. We also include aperture-matched ZYJHK s photometry from our partner VIKING survey on the VISTA telescope in the photometry catalogue. We illustrate the data quality and describe the catalogue content. Methods. Two dedicated pipelines are used for the production of the optical data. The Astro-WISE information system is used for the production of co-added images in the four survey bands, while a separate reduction of the r-band images using the theli pipeline is used to provide a source catalogue suitable for the core weak lensing science case. All data have been re-reduced for this data release using the latest versions of the pipelines. The VIKING photometry is obtained as forced photometry on the theli sources, using a re-reduction of the VIKING data that starts from the VISTA pawprints. Modifications to the pipelines with respect to earlier releases are described in detail. The photometry is calibrated to the Gaia DR2 G band using stellar locus regression. Results. In this data release a total of 1006 square-degree survey tiles with stacked ugri images are made available, accompanied by weight maps, masks, and single-band source lists. We also provide a multi-band catalogue based on r-band detections, including homogenized photometry and photometric redshifts, for the whole dataset. Mean limiting magnitudes (5σ in a 2 aperture) and the tile-to-tile rms scatter are 24.23 ± 0.12, 25.12 ± 0.14, 25.02 ± 0.13, 23.68 ± 0.27 in ugri, respectively, and the mean r-band seeing is 0 . 70.