Higher-Order Spectra of Weak Lensing Convergence Maps in Parameterized Theories of Modified Gravity

We compute the low-$\ell$ limit of the family of higher-order spectra for projected (2D) weak lensing convergence maps. In this limit, these spectra are computed to an arbitrary order using {\em tree-level} perturbative calculations. We use the flat-sky approximation and Eulerian perturbative results based on a generating function approach. We test these results for the lower-order members of this family, i.e. the skew- and kurt-spectra against state-of-the-art simulated all-sky weak lensing convergence maps and find our results to be in very good agreement. We also show how these spectra can be computed in the presence of a realistic sky-mask and Gaussian noise. We generalize these results to three-dimensions (3D) and compute the {\em equal-time} higher-order spectra. These results will be valuable in analyzing higher-order statistics from future all-sky weak lensing surveys such as the {\em Euclid} survey at low-$\ell$ modes. As illustrative examples, we compute these statistics in the context of the {\em Horndeski} and {\em Beyond Horndeski} theories of modified gravity. They will be especially useful in constraining theories such as the Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories and Degenerate Higher-Order Scalar-Tensor (DHOST) theories as well as the commonly used normal-branch of Dvali-Gabadadze-Porrati (nDGP) model, clustering quintessence models, and scenarios with massive neutrinos.