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

¹ Laboratoire AIM, UMR CEA-CNRS-Paris 7, Irfu, Service d’Astrophysique, CEA Saclay, 91191 Gif-sur-Yvette, France
e-mail: austin.peel@cea.fr
² McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
³ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁴ Institut d’Astrophysique de Paris, CNRS UMR 7095 & UPMC, 98bis boulevard Arago, 75014 Paris, France

Received: 18 October 2016
Accepted: 15 December 2016

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, σ₈, and w₀^de. 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 deg² using a multiscale mass-map filtering technique. We constrain the parameters of the mock survey using Camelus combined with approximate Bayesian computation, a robust likelihood-free inference algorithm. Peak statistics yield a tight but significantly biased constraint in the σ₈–Ω_m plane, as measured by the width ΔΣ₈ of the 1σ contour. We find Σ₈ = σ₈(Ω_m/ 0.27)^α = 0.77_-0.05^+0.06 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 Σ₈ = 0.76_-0.03^+0.02 with α = 0.65, while for the combined ξ₊ and ξ₋ statistics the values are Σ₈ = 0.76_-0.01^+0.02 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 σ₈–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, w₀^de 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_±.