Estimating the Integrated Bispectrum from Weak Lensing Maps

We use a recently introduced statistic called {\em Integrated Bispectrum} (IB) to probe the gravity-induced non-Gaussianity at the level of the bispectrum from weak lensing convergence or $\kappa$ maps. We generalize the concept of the IB to spherical coordinates. This result is next connected to the response function approach. Finally, we use the Euclid Flagship simulations to compute the IB as a function of redshift and wave number. We also outline how the IB can be computed using a variety of analytical approaches including the ones based on Effective Field Theory (EFT), {\em Halo models} and models based on the {\em Separate Universe approach} in projection or two-dimension (2D). Comparing these results against simulations we find that the existing theoretical models tend to over-predict the numerical value of the IB. We emphasize the role of the finite volume effect in the numerical estimation of the IB. We introduced the concept of squeezed and collapsed tripsectrum for 2D $\kappa$ maps. We derive the IB for many parameterized theories of modified gravity including the Horndeskii and beyond-Horndeskii theories specifically for the non-degenerate scenarios that are also known as the Gleyzes-Langlois-Piazza-Venizzi or GPLV theories. In addition, the cosmological models with clustering quintessence and models involving massive neutrinos are also derived.