Cosmology with the shear-peak statistics

Weak-lensing searches for galaxy clusters are plagued by low completeness and purity, severely limiting their usefulness for constraining cosmological parameters with the cluster mass function. A significant fraction of `false positives' are due to projection of large-scale structure and as such carry information about the matter distribution. We demonstrate that by constructing a `peak function', in analogy to the cluster mass function, cosmological parameters can be constrained. To this end, we carried out a large number of cosmological N-body simulations in the Ω_m-σ₈ plane to study the variation of this peak function. We demonstrate that the peak statistics is able to provide constraints competitive with those obtained from cosmic-shear tomography from the same data set. By taking the full cross-covariance between the peak statistics and cosmic shear into account, we show that the combination of both methods leads to tighter constraints than either method alone can provide.