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 \Omega _ { \mathrm { m } } , \sigma _ { 8 } , and w _ { 0 } ^ { \mathrm { 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 signal-to-noise \geq 1 , we measure the abundance histogram in a mock shear catalogue of approximately 5 000 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 likelihood-free inference algorithm .
Peak statistics yield a tight but significantly biased constraint in the \sigma _ { 8 } – \Omega _ { \mathrm { m } } plane , as measured by the width \Delta \Sigma _ { 8 } of the 1- \sigma contour .
We find \Sigma _ { 8 } = \sigma _ { 8 } ( \Omega _ { \mathrm { m } } / 0.27 ) ^ { \alpha } = 0.77 _ { -0.05 } ^ { +0.06 } with \alpha = 0.75 for a flat \Lambda CDM model .
The strong bias indicates the need to better understand and control the model ’ s 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 \xi _ { \pm } measured on the same field .
We calibrate the \xi _ { \pm } result as well , since its contours are also biased , although not as severely as for peaks .
In this case , we find for peaks \Sigma _ { 8 } = 0.76 _ { -0.03 } ^ { +0.02 } with \alpha = 0.65 , while for the combined \xi _ { + } and \xi _ { - } statistics the values are \Sigma _ { 8 } = 0.76 _ { -0.01 } ^ { +0.02 } and \alpha = 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 \sigma _ { 8 } – \Omega _ { \mathrm { m } } degeneracy direction for peaks with respect to that of \xi _ { \pm } suggests that a combined analysis would yield tighter constraints than either measure alone .
As expected , w _ { 0 } ^ { \mathrm { de } } can not be well constrained without a tomographic analysis , but its degeneracy directions with the other two varied parameters are still clear for both peaks and \xi _ { \pm } .