Galaxy cluster lensing masses in modified lensing potentials

We determine the concentration-mass relation of 19 X-ray selected galaxy clusters from the CLASH survey in theories of gravity that directly modify the lensing potential. We model the clusters as NFW haloes and fit their lensing signal, in the Cubic Galileon and Nonlocal gravity models, to the lensing convergence profiles of the clusters. We discuss a number of important issues that need to be taken into account, associated with the use of nonparametric and parametric lensing methods, as well as assumptions about the background cosmology. Our results show that the concentration and mass estimates in the modified gravity models are, within the errorbars, the same as in $\Lambda$CDM. This result demonstrates that, for the Nonlocal model, the modifications to gravity are too weak at the cluster redshifts, and for the Galileon model, the screening mechanism is very efficient inside the cluster radius. However, at distances $\sim \left[2-20\right] {\rm Mpc}/h$ from the cluster center, we find that the surrounding force profiles are enhanced by $\sim20-40\%$ in the Cubic Galileon model. This has an impact on dynamical mass estimates, which means that tests of gravity based on comparisons between lensing and dynamical masses can also be applied to the Cubic Galileon model.