KiDS-Legacy: Cosmological constraints from cosmic shear with the complete Kilo-Degree Survey

We present cosmic shear constraints from the completed Kilo-Degree Survey (KiDS), where the cosmological parameter S ₈ ≡ σ ₈√Ω_m/0.3 = 0.81^+0.016_−0.021 is found to be in agreement (0.73σ) with results from the Planck Legacy cosmic microwave background experiment. The final KiDS footprint spans 1347 square degrees of deep nine-band imaging across the optical and near-infrared (NIR), along with an extra 23-square degrees of KiDS-like calibration observations of deep spectroscopic surveys. Improvements in our redshift distribution estimation methodology, combined with our enhanced calibration data and multi-band image simulations, allowed us to extend our lensed sample out to a photometric redshift of z _B ≤ 2.0. Compared to previous KiDS analyses, the increased survey area and redshift depth results in a ∼32% improvement in constraining power in terms of Σ₈ ≡ σ ₈(Ω_m/0.3)^α = 0.821^+0.014_−0.016, where α = 0.58 has been optimised to match the revised degeneracy direction of σ ₈ and Ω_m for our current survey at higher redshift. We adopted a new physically motivated intrinsic alignment (IA) model that jointly depends on the galaxy sample’s halo mass and spectral type distributions, and which is informed by previous direct alignment measurements. We also marginalised over our uncertainty on the impact of baryon feedback on the non-linear matter power spectrum. Compared to previous KiDS analyses, we conclude that the increase seen in S ₈ primarily results from our improved redshift distribution estimation and calibration, as well as a new survey area and improved image reduction. Our companion paper presents a full suite of internal and external consistency tests (including joint constraints with other datasets), finding the KiDS-Legacy dataset to be the most internally robust sample produced by KiDS to date.