The unprecedented quality, the increased dataset, and the wide area of ongoing and near future weak lensing surveys allows to move beyond the standard two points statistics thus making worthwhile to investigate higher order probes. As an interesting step towards this direction, we expolore the use of higher order moments (HOM) of the convergence field as a way to increase the lensing Figure of Merit (FoM). To this end, we rely on simulated convergence to first show that HOM can be measured and calibrated so that it is indeed possible to predict them for a given cosmological model provided suitable nuisance parameters are introduced and then marginalized over. We then forecast the accuracy on cosmological parameters from the use of HOM alone and in combination with standard shear power spectra tomography. It turns out that HOM allow to break some common degeneracies thus significantly boosting the overall FoM. We also qualitatively discuss possible systematics and how they can be dealt with.
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