General relativity (GR) has been well tested up to solar system scales, but it is much less certain that standard gravity remains an accurate description on the largest, that is, cosmological, scales. Many extensions to GR have been studied that are not yet ruled out by the data, including by that of the recent direct gravitational wave detections. Degeneracies among the standard model ($\Lambda$CDM) and modified gravity (MG) models, as well as among different MG parameters, must be addressed in order to best exploit information from current and future surveys and to unveil the nature of dark energy. We propose various higher-order statistics in the weak-lensing signal as a new set of observables able to break degeneracies between massive neutrinos and MG parameters. We have tested our methodology on so-called $f(R)$ models, which constitute a class of viable models that can explain the accelerated universal expansion by a modification of the fundamental gravitational interaction. We have explored a range of these models that still fit current observations at the background and linear level, and we show using numerical simulations that certain models which include massive neutrinos are able to mimic $\Lambda$CDM in terms of the 3D power spectrum of matter density fluctuations. We find that depending on the redshift and angular scale of observation, non-Gaussian information accessed by higher-order weak-lensing statistics can be used to break the degeneracy between $f(R)$ models and $\Lambda$CDM. In particular, peak counts computed in aperture mass maps outperform third- and fourth-order moments.

We present ClumPyLen, a Python-based simulator designed to produce realistic mock observations of strongly lensed, high-redshift, clumpy star-forming galaxies. The tool models galaxy components such as disks, bulges, and spiral arms using Sérsic profiles, and it populates them with stellar clumps whose properties are sampled from physically motivated distributions. ClumPyLen includes the effects of gravitational lensing through user-provided deflection angle maps and simulates realistic observational conditions by accounting for instrumental effects, Point-Spread-Function convolution, sky background, and photon noise. The simulator can support a wide range of filters and instruments; here we focus on HST/ACS, HST/WFC3-IR, and JWST/NIRCam. We demonstrate the capabilities of the code through two examples, including a detailed simulation of the z = 6.145 source Cosmic Archipelago lensed by MACS J0416.1-2403. The simulated images closely match the morphology and limiting magnitudes of real observations. ClumPyLen is designed to explore the detectability of stellar clumps in terms of mass and size, especially in the low-mass regime, and it allows the study of clump blending effects. Thanks to its modular design, the code is highly adaptable to a wide range of scientific goals, including lensing studies, galaxy evolution, and the generation of synthetic datasets for machine learning or forward modeling applications.