# KiDS-450: The tomographic weak lensing power spectrum and constraints on cosmological parameters

## TL;DR

This paper measures the weak lensing shear power spectrum from the KiDS-450 survey, constrains cosmological parameters within a Bayesian framework, and finds a tension with Planck results in the parameter S8.

## Contribution

It provides the first detailed tomographic shear power spectrum analysis of KiDS-450 data with comprehensive modeling of systematics and inclusion of massive neutrinos.

## Key findings

- Measured shear power spectra in multiple redshift bins.
- Found S8 = 0.651 ± 0.058, indicating tension with Planck.
- Confirmed consistency between 2- and 3-bin analyses.

## Abstract

We present measurements of the weak gravitational lensing shear power spectrum based on $450$ sq. deg. of imaging data from the Kilo Degree Survey. We employ a quadratic estimator in two and three redshift bins and extract band powers of redshift auto-correlation and cross-correlation spectra in the multipole range $76 \leq \ell \leq 1310$. The cosmological interpretation of the measured shear power spectra is performed in a Bayesian framework assuming a $\Lambda$CDM model with spatially flat geometry, while accounting for small residual uncertainties in the shear calibration and redshift distributions as well as marginalising over intrinsic alignments, baryon feedback and an excess-noise power model. Moreover, massive neutrinos are included in the modelling. The cosmological main result is expressed in terms of the parameter combination $S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ yielding $S_8 = \ 0.651 \pm 0.058$ (3 z-bins), confirming the recently reported tension in this parameter with constraints from Planck at $3.2\sigma$ (3 z-bins). We cross-check the results of the 3 z-bin analysis with the weaker constraints from the 2 z-bin analysis and find them to be consistent. The high-level data products of this analysis, such as the band power measurements, covariance matrices, redshift distributions, and likelihood evaluation chains are available at http://kids.strw.leidenuniv.nl/