Weak lensing statistics from the Coyote Universe

Analyzing future weak lensing data sets from KIDS, DES, LSST, Euclid, 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_delta) to high accuracy for k \in [0.002;3.4] h/Mpc within the redshift interval z \in [0;1], outside this regime we extend P_delta 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 COSEBIs (Complete Orthogonal Set of EB-mode Integrals), and we examine how the upper limit in k (and z) to which P_delta is known, impacts on these statistics. For example, we find that k_max~8 h/Mpc 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~15 h/Mpc is needed to limit the bias at l~4000. For the most recently developed second-order shear statistics, the COSEBIs, we find that 9 modes can be calculated accurately knowing P_delta to k_max=10 h/Mpc. 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 5-dimensional parameter space in order to examine whether all cosmological information is captured by these 9 modes with the result that already 7-8 modes are sufficient.