We propose counting peaks in weak lensing (WL) maps, as a function of their height, to probe models of dark energy and to constrain cosmological parameters. Because peaks can be identified in two-dimensional WL maps directly, they can provide constraints that are free from potential selection effects and biases involved in identifying and determining the masses of galaxy clusters. As a pilot study, we have run cosmological N-body simulations to produce WL convergence maps in three models with different constant values of the dark energy equation-of-state parameter, $w=-0.8$, $-1$, and $-1.2$, with a fixed normalization of the primordial power spectrum (corresponding to present-day normalizations of ${\sigma }_8=0.742$, 0.798, and 0.839, respectively). By comparing the number of WL peaks in eight convergence bins in the range of $-0.1<\kappa <0.4$, in multiple realizations of a single simulated $3\times 3$ degree field, we show that the first (last) pair of models differ at the 95% (85%) confidence level. A survey with depth and area comparable to those expected from the Large Synoptic Survey Telescope should have a factor of $\approx 50$ better parameter sensitivity. These results warrant further investigation, in order to assess the constraints available when marginalization over other uncertain parameters is included, and with the specifications of a realistic survey folded into the analysis. Here we find that relatively low-amplitude peaks ($\kappa \sim 0.03$), which typically do not correspond to a single collapsed halo along the line of sight, account for most of the parameter sensitivity. We study a range of smoothing scales and source galaxy redshifts ($z_s$). With a fixed source galaxy density of $15{\mathrm{arcmin}}^{-2}$, the best results are provided by the smallest scale we can reliably simulate, 1 arcmin, and $z_s=2$ provides substantially better sensitivity than $z_s\le 1.5$.

• Received 5 July 2009

DOI:https://doi.org/10.1103/PhysRevD.81.043519