Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey

Abstract

Peak statistics in weak-lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complementary probe to two-point and higher-order statistics to constrain our cosmological models. Next-generation galaxy surveys, with their advanced optics and large areas, will measure the cosmic weak-lensing signal with unprecedented precision. To prepare for these anticipated data sets, we assess the constraining power of peak counts in a simulated Euclid-like survey on the cosmological parameters Ω m , σ 8 , and w de 0 . In particular, we study how Camelus, a fast stochastic model for predicting peaks, can be applied to such large surveys. The algorithm avoids the need for time-costly N-body simulations, and its stochastic approach provides full PDF information of observables. Considering peaks with a signal-to-noise ratio ≥1, we measure the abundance histogram in a mock shear catalogue of approximately 5000 deg 2 using a multiscale mass-map filtering technique. We constrain the parameters of the mock survey using Camelus combined with approximate Bayesian computation, a robust likelihoodfree inference algorithm. Peak statistics yield a tight but significantly biased constraint in the σ 8 -Ω m plane, as measured by the width ∆Σ 8 of the 1σ contour. We find Σ 8 = σ 8 (Ω m /0.27) α = 0.77−0.05 with α = 0.75 for a flat ΛCDM model. The strong bias indicates the need to better understand and control the model systematics before applying it to a real survey of this size or larger. We perform a calibration of the model and compare results to those from the two-point correlation functions ξ ± measured on the same field. We calibrate the ξ ± result as well, since its contours are also biased, although not as severely as for peaks. In this case, we find for peaks Σ 8 = 0.76 −0.01 and α = 0.70. We conclude that the constraining power can therefore be comparable between the two weak-lensing observables in large-field surveys. Furthermore, the tilt in the σ 8 -Ω m degeneracy direction for peaks with respect to that of ξ ± suggests that a combined analysis would yield tighter constraints than either measure alone. As expected, w de 0 cannot be well constrained without a tomographic analysis, but its degeneracy directions with the other two varied parameters are still clear for both peaks and ξ ± .

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