Weak-lensing statistics from the Coyote Universe

Analysing future weak-lensing data sets from KIDS, Dark Energy Survey (DES), LSST, Euclid and WFIRST requires precise predictions for the weak-lensing measures. In this paper, we present a weak-lensing prediction code based on the Coyote Universe emulator. The Coyote Universe emulator predicts the (non-linear) power spectrum of density fluctuations (P_δ) to high accuracy for k∈[0.002; 3.4]hMpc^-1 within the redshift interval z∈[0; 1]; outside this regime, we extend P_δ using a modified halofit code. This pipeline is used to calculate various second-order cosmic shear statistics, e.g., shear power spectrum, shear-shear correlation function, ring statistics and Complete Orthogonal Set of EB-mode Integrals (COSEBIs), and we examine how the upper limit in k (and z), to which P_δ is known, impacts on these statistics. For example, we find that k_max∼ 8hMpc^-1 causes a bias in the shear power spectrum at ℓ∼ 4000 that is comparable to the statistical errors (intrinsic shape noise and cosmic variance) of a DES-like survey, whereas for LSST-like errors k_max∼ 15hMpc^-1 is needed to limit the bias at ℓ∼ 4000. For the most recently developed second-order shear statistics, the COSEBIs, we find that nine modes can be calculated accurately knowing P_δ to k_max= 10hMpc^-1. The COSEBIs allow for an EB-mode decomposition using a shear-shear correlation function measured over a finite range, thereby avoiding any EB-mode mixing due to finite survey size. We perform a detailed study in a five-dimensional parameter space in order to examine whether all cosmological information is captured by these nine modes with the result that already 7-8 modes are sufficient.