We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ∼450 deg 2 of imaging data from the Kilo Degree Survey (KiDS). For a flat ΛCDM cosmology with a prior on H 0 that encompasses the most recent direct measurements, we find S 8 ≡ σ 8 Ω m /0.3 = 0.745 ± 0.039. This result is in good agreement with other low redshift probes of large scale structure, including recent cosmic shear results, along with pre-Planck cosmic microwave background constraints. A 2.3σ tension in S 8 and 'substantial discordance' in the full parameter space is found with respect to the Planck 2015 results. We use shear measurements for nearly 15 million galaxies, determined with a new improved 'self-calibrating' version of lensfit validated using an extensive suite of image simulations. Four-band ugri photometric redshifts are calibrated directly with deep spectroscopic surveys. The redshift calibration is confirmed using two independent techniques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an analytical approach, verified numerically with large mock galaxy catalogues. We account for uncertainties in the modelling of intrinsic galaxy alignments and the impact of baryon feedback on the shape of the non-linear matter power spectrum, in addition to the small residual uncertainties in the shear and redshift calibration. The cosmology analysis was performed blind. Our high-level data products, including shear correlation functions, covariance matrices, redshift distributions, and Monte Carlo Markov Chains are available at http://kids.strw.leidenuniv.nl.

We present an optimized variant of the halo model, designed to produce accurate matter power spectra well into the non-linear regime for a wide range of cosmological models. To do this, we introduce physically motivated free parameters into the halo-model formalism and fit these to data from high-resolution N-body simulations. For a variety of ΛCDM and wCDM models the halo-model power is accurate to ≃ 5 per cent for k ≤ 10h Mpc −1 and z ≤ 2. An advantage of our new halo model is that it can be adapted to account for the effects of baryonic feedback on the power spectrum. We demonstrate this by fitting the halo model to power spectra from the OWLS hydrodynamical simulation suite via parameters that govern halo internal structure. We are able to fit all feedback models investigated at the 5 per cent level using only two free parameters, and we place limits on the range of these halo parameters for feedback models investigated by the OWLS simulations. Accurate predictions to high-k are vital for weak lensing surveys, and these halo parameters could be considered nuisance parameters to marginalize over in future analyses to mitigate uncertainty regarding the details of feedback. Finally, we investigate how lensing observables predicted by our model compare to those from simulations and from HALOFIT for a range of k-cuts and feedback models and quantify the angular scales at which these effects become important. Code to calculate power spectra from the model presented in this paper can be found at https://github.com/alexander-mead/hmcode.

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 perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg 2 of imaging data by the Kilo Degree Survey (KiDS-450) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of N -body simulations. We methodically analyze different combinations of the observables, finding that galaxy-galaxy lensing measurements are particularly useful in improving the constraint on the intrinsic alignment amplitude (by 30%, positive at 3.5σ in the fiducial data analysis), while the multipole power spectra are useful in tightening the constraints along the lensing degeneracy direction (e.g. factor of two improvement in the matter density constraint in the fiducial analysis). The fully combined constraint on S 8 ≡ σ 8 Ω m /0.3 = 0.742 ± 0.035, which is an improvement by 20% compared to KiDS alone, corresponds to a 2.6σ discordance with Planck, and is not significantly affected by fitting to a more conservative set of scales. Given the tightening of the parameter space, we are unable to resolve the discordance with an extended cosmology that is simultaneously favored in a model selection sense, including the sum of neutrino masses, curvature, evolving dark energy (both constant and time-varying equations of state), and modified gravity. The complementarity of our observables allows for constraints on modified gravity degrees of freedom that are not simultaneously bounded with either probe alone, and up to a factor of three improvement in the S 8 constraint in the extended cosmology compared to KiDS alone. We make our measurements and fitting pipeline public at https://github.com/sjoudaki/CosmoLSS.