Gravitational lensing from clusters of galaxies to test Disformal Couplings Theories

In this study, we investigate the potential existence of a non-minimal coupling between dark matter and gravity using a compilation of galaxy clusters. We focus on the disformal scenario of a non-minimal model with an associated coupling length $L$. Within the Newtonian approximation, this model introduces a modification to the Poisson equation, characterized by a term proportional to $L^2 \nabla^2 \rho$, where $\rho$ represents the density of the DM field. We have tested the model by examining strong and weak gravitational lensing data available for a selection of 19 high-mass galaxy clusters observed by the CLASH survey. We have employed a Markov Chain Monte Carlo code to explore the parameter space, and two different statistical approaches to analyse our results: a standard marginalisation and a profile distribution method. Notably, the profile distribution analysis helps out to bypass some volume-effects in the posterior distribution, and reveals lower Navarro--Frenk--White concentrations and masses in the non-minimal coupling model compared to general relativity case. We also found a nearly perfect correlation between the coupling constant $L$ and the standard Navarro--Frenk--White scale parameter $r_s$, hinting at a compelling link between these two lengths.