KiDS-1000 Cosmology: Constraints beyond flat ?CDM

We present constraints on extensions to the standard cosmological model of a spatially flat Universe governed by general relativity, constant (?), and cold dark matter (CDM) varying spatial curvature ? K , sum neutrino masses ? m ? energy equation state parameter w Hu-Sawicki f ( R ) gravity 0 parameter. With combined 3 × 2 pt measurements cosmic shear from Kilo-Degree Survey (KiDS-1000), galaxy clustering Baryon Oscillation Spectroscopic (BOSS), galaxy-galaxy lensing overlap between KiDS-1000, BOSS, spectroscopic 2-degree Field Lensing Survey, we find results that are fully consistent with ?CDM = 0.011 ?0.057 +0.054 < 1.76 eV (95% CL), ?0.99 ?0.13 +0.11 . The is unconstrained in our non-linear analysis. Considering three different selection criteria, no clear preference for either fiducial or any considered extensions. In addition space, also explore restrictions common subsets space fixing amplitude primordial power spectrum Planck best-fit value, as well adding external data supernovae microwave background (CMB). Neither beyond-?CDM models nor imposed explored this analysis able resolve ?3 ? tension S 8 temperature polarisation data, exception CDM, where resolved. CDM case persists, however, when considering joint ? space. CMB found yield tight 0.307 ?0.013 +0.008 0.769 ?0.010 +0.022 0.779 +0.013