KiDS-450: Cosmological parameter constraints from tomographic weak gravitational lensing

We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ~450 deg² of imaging data from the Kilo Degree Survey (KiDS). For a flat λCDM cosmology with a prior on H₀ that encompasses the most recent direct measurements, we find S₈ ≡ σ₈ √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 2.3-σ tension in S₈ 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 lens fit 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 tech- niques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an analytical approach, verified numeri- cally 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.