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General relativity (GR) has been well tested up to solar system scales, butit is much less certain that standard gravity remains an accurate descriptionon the largest, that is, cosmological, scales. Many extensions to GR have beenstudied that are not yet ruled out by the data, including by that of the recentdirect gravitational wave detections. Degeneracies among the standard model($\Lambda$CDM) and modified gravity (MG) models, as well as among different MGparameters, must be addressed in order to best exploit information from currentand future surveys and to unveil the nature of dark energy. We propose varioushigher-order statistics in the weak-lensing signal as a new set of observablesable to break degeneracies between massive neutrinos and MG parameters. We havetested our methodology on so-called $f(R)$ models, which constitute a class ofviable models that can explain the accelerated universal expansion by amodification of the fundamental gravitational interaction. We have explored arange of these models that still fit current observations at the background andlinear level, and we show using numerical simulations that certain models whichinclude massive neutrinos are able to mimic $\Lambda$CDM in terms of the 3Dpower spectrum of matter density fluctuations. We find that depending on theredshift and angular scale of observation, non-Gaussian information accessed byhigher-order weak-lensing statistics can be used to break the degeneracybetween $f(R)$ models and $\Lambda$CDM. In particular, peak counts computed inaperture mass maps outperform third- and fourth-order moments.

Breaking degeneracies in modified gravity with higher (than 2nd) order weak-lensing statistics