KiDS & Euclid: Cosmological implications of a pseudo angular power spectrum analysis of KiDS-1000 cosmic shear tomography

We present a tomographic weak lensing analysis of the Kilo Degree Survey Data Release 4 (KiDS-1000) using a new pseudo angular power spectrum estimator (\pcl) under development for the ESA Euclid mission. Over 21 million galaxies with shape information are divided into five tomographic redshift bins ranging from 0.1 to 1.2 in photometric redshift. We measure \pcl{} using eight bands in the multipole range $76<\ell<1500$ for auto- and cross-power spectra between the tomographic bins. A series of tests are carried out to check for systematic contamination from a variety of observational sources including stellar number density, variations in survey depth, and point spread function properties. While some marginal correlations with these systematic tracers are observed, there is no evidence of bias in the cosmological inference. B-mode power spectra are consistent with zero signal, with no significant residual contamination from E/B-mode leakage. We perform a Bayesian analysis of the \pcl{} estimates by forward-modelling the effects of the mask. Assuming a spatially flat \lcdm{} cosmology, we constrain the structure growth parameter $S_8 = \sigma_8(\Omega_{\rm m}/0.3)^{1/2} = 0.754_{-0.029}^{+0.027}$. When combining cosmic shear from KiDS-1000 with baryon acoustic oscillation and redshift space distortion data from recent Sloan Digital Sky Survey (SDSS) measurements of luminous red galaxies, as well as the Lyman-$\alpha$ forest and its cross-correlation with quasars, we tighten these constraints to $S_8 = 0.771^{+0.006}_{-0.032}$. These results are in very good agreement with previous KiDS-1000 and SDSS analyses and confirm a $\sim 3\sigma$ tension with early-Universe constraints from cosmic microwave background experiments.