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 a tomographic cosmic shear analysis of the Kilo-Degree Survey (KiDS) combined with the VISTA Kilo-Degree Infrared Galaxy Survey (VIKING). This is the first time that a full optical to near-infrared data set has been used for a wide-field cosmological weak lensing experiment. This unprecedented data, spanning 450 deg 2 , allows us to improve significantly the estimation of photometric redshifts, such that we are able to include robustly higher-redshift sources for the lensing measurement, and -most importantly -solidify our knowledge of the redshift distributions of the sources. Based on a flat ΛCDM model we find S 8 ≡ σ 8√ Ω m /0.3 = 0.737 +0.040 −0.036 in a blind analysis from cosmic shear alone. The tension between KiDS cosmic shear and the Planck-Legacy CMB measurements remains in this systematically more robust analysis, with S 8 differing by 2.3σ. This result is insensitive to changes in the priors on nuisance parameters for intrinsic alignment, baryon feedback, and neutrino mass. KiDS shear measurements are calibrated with a new, more realistic set of image simulations and no significant B-modes are detected in the survey, indicating that systematic errors are under control. When calibrating our redshift distributions by assuming the 30-band COSMOS-2015 photometric redshifts are correct (following the Dark Energy Survey and the Hyper Suprime-Cam Survey), we find the tension with Planck is alleviated. The robust determination of source redshift distributions remains one of the most challenging aspects for future cosmic shear surveys. Data products from this analysis are available at http://kids.strw.leidenuniv.nl.

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.

We present a combined tomographic weak gravitational lensing analysis of the Kilo Degree Survey (KV450) and the Dark Energy Survey (DES-Y1). We homogenize the analysis of these two public cosmic shear datasets by adopting consistent priors and modeling of nonlinear scales, and determine new redshift distributions for DES-Y1 based on deep public spectroscopic surveys. Adopting these revised redshifts results in a 0.8σ reduction in the DES-inferred value for S​8, which decreases to a 0.5σ reduction when including a systematic redshift calibration error model from mock DES data based on the MICE2 simulation. The combined KV450+DES-Y1 constraint on S8 = 0.762−0.024+0.025 is in tension with the Planck 2018 constraint from the cosmic microwave background at the level of 2.5σ. This result highlights the importance of developing methods to provide accurate redshift calibration for current and future weak-lensing surveys.