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Large area lensing surveys are expected to make it possible to use cosmic shear tomography as a tool to severely constrain cosmological parameters. To this end, one typically relies on second order statistics such as the two - point correlation fucntion and its Fourier counterpart, the power spectrum. Moving a step forward, we wonder whether and to which extent higher order stastistics can improve the lensing Figure of Merit (FoM). In this first paper of a series, we investigate how second, third and fourth order lensing convergence moments can be measured and use as probe of the underlying cosmological model. We use simulated data and investigate the impact on moments estimate of the map reconstruction procedure, the cosmic variance, and the intrinsic ellipticity noise. We demonstrate that, under realistic assumptions, it is indeed possible to use higher order moments as a further lensing probe.
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
We compare the efficiency of moments and Minkowski functionals (MFs) in constraining the subset of cosmological parameters (Omega_m,w,sigma_8) using simulated weak lensing convergence maps. We study an analytic perturbative expansion of the MFs in te
Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has proven to
A calculation method for higher-order moments of physical quantities, including magnetization and energy, based on the higher-order tensor renormalization group is proposed. The physical observables are represented by impurity tensors. A systematic s
Gravitational lensing surveys have now become large and precise enough that the interpretation of the lensing signal has to take into account an increasing number of theoretical limitations and observational biases. Since the lensing signal is the st