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This paper is the first of a series of papers constraining cosmologicalparameters with weak lensing peak statistics using $\sim 450~\rm deg^2$ ofimaging data from the Kilo Degree Survey (KiDS-450). We measure highsignal-to-noise ratio (SNR: $\nu$) weak lensing convergence peaks in the rangeof $3<\nu<5$, and employ theoretical models to derive expected values. Thesemodels are validated using a suite of simulations. We take into account twomajor systematic effects, the boost factor and the effect of baryons on themass-concentration relation of dark matter haloes. In addition, we investigatethe impacts of other potential astrophysical systematics including theprojection effects of large scale structures, intrinsic galaxy alignments, aswell as residual measurement uncertainties in the shear and redshiftcalibration. Assuming a flat $\Lambda$CDM model, we find constraints for$S_{\rm 8}=\sigma_{\rm 8}(\Omega_{\rm m}/0.3)^{0.5}=0.746^{+0.046}_{-0.107}$according to the degeneracy direction of the cosmic shear analysis and$\Sigma_{\rm 8}=\sigma_{\rm 8}(\Omega_{\rmm}/0.3)^{0.38}=0.696^{+0.048}_{-0.050}$ based on the derived degeneracydirection of our high-SNR peak statistics. The difference between the powerindex of $S_{\rm 8}$ and in $\Sigma_{\rm 8}$ indicates that combining the twoprobes has the potential to break the degeneracy in $\sigma_{\rm 8}$ and$\Omega_{\rm m}$. Our results are consistent with the cosmic shear tomographiccorrelation analysis of the same dataset and $\sim 2\sigma$ lower than thePlanck 2016 results.

monthly notices of the royal astronomical society

KiDS-450: Cosmological Constraints from Weak Lensing Peak Statistics-I:  Inference from Analytical Prediction of High Signal-to-Noise Ratio  Convergence Peaks