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 del 2 rho \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>2 \nabla <^>2 \rho $$\end{document} , where rho \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_s$$\end{document} , hinting at a compelling link between these two lengths.