## Abstract

We present a new method to extract cosmological constraints from weak lensing (WL) peak counts, which we denote as ‘the hierarchical algorithm’. The idea of this method is to combine information from WL maps sequentially smoothed with a series of filters of different size, from the largest down to the smallest, thus increasing the cosmological sensitivity of the resulting peak function. We compare the cosmological constraints resulting from the peak abundance measured in this way and the abundance obtained by using a filter of fixed size, which is the standard practice in WL peak studies. For this purpose, we employ a large set of WL maps generated by ray tracing through N-body simulations, and the Fisher matrix formalism. We find that if low signal-to-noise ratio (?) peaks are included in the analysis (?), the hierarchical method yields constraints significantly better than the single-sized filtering. For a large future survey such as Euclid or Large Synoptic Survey Telescope, combined with information from a cosmic microwave background experiment like Planck, the results for the hierarchical (single-sized) method are Δns= 0.0039 (0.004), ΔΩm= 0.002 (0.0045), Δσ8= 0.003 (0.006) and Δw= 0.019 (0.0525). This forecast is conservative, as we assume no knowledge of the redshifts of the lenses, and consider a single broad bin for the redshifts of the sources. If only peaks with ? are considered, then there is little difference between the results of the two methods. We also examine the statistical properties of the hierarchical peak function: Its covariance matrix has off-diagonal terms for bins with ? and aperture mass of M < 3 × 1014 h-1 Msun, the higher bins being largely uncorrelated and therefore well described by a Poisson distribution.