KiDS-450: cosmological constraints from weak lensing peak statistics - I. Inference from analytical prediction of high signal-to-noise ratio convergence peaks

This paper is the first of a series of papers constraining cosmological parameters with weak lensing peak statistics using ∼ 450 deg² of imaging data from the Kilo Degree Survey (KiDS-450). We measure high signal-to-noise ratio (SNR: ν) weak lensing convergence peaks in the range of 3 < ν < 5, and employ theoretical models to derive expected values. These models are validated using a suite of simulations. We take into account two major systematic effects, the boost factor and the effect of baryons on the mass-concentration relation of dark matter haloes. In addition, we investigate the impacts of other potential astrophysical systematics including the projection effects of large-scale structures, intrinsic galaxy alignments, as well as residual measurement uncertainties in the shear and redshift calibration. Assuming a flat Λ cold dark matter model, we find constraints for S_8=σ _8(Ω _m/0.3)^{0.5}=0.746^{+0.046}_{-0.107} according to the degeneracy direction of the cosmic shear analysis and Σ _8=σ _8(Ω _m/0.3)^{0.38}=0.696^{+0.048}_{-0.050} based on the derived degeneracy direction of our high-SNR peak statistics. The difference between the power index of S₈ and in Σ₈ indicates that combining cosmic shear with peak statistics has the potential to break the degeneracy in σ₈ and Ω_m. Our results are consistent with the cosmic shear tomographic correlation analysis of the same data set and ∼2σ lower than the Planck 2016 results.