SIMBAD references

We compute the low-l 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 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 3D and compute the equal-time higher order spectra. These results will be valuable in analysing higher order statistics from future all-sky weak lensing surveys such as the Euclid survey at low-l modes. As illustrative examples, we compute these statistics in the context of the Horndeski and 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 theories as well as the commonly used normal-branch of Dvali-Gabadadze-Porrati model, clustering quintessence models and scenarios with massive neutrinos.