Modified gravity theories with a screening mechanism have acquired much
interest recently in the quest for a viable alternative to General Relativity
on cosmological scales, given their intrinsic property of being able to pass
Solar System scale tests and, at the same time, to possibly drive universe
acceleration on much larger scales. Here, we explore the possibility that the
same screening mechanism, or its partial breaking at a certain astrophysical
scale, might be responsible of those gravitational effects which, in the
context of general relativity, are generally attributed to Dark Matter. We
consider a recently proposed extension of covariant Galileon models in the
so-called "beyond Horndeski" scenario, where a breaking of the Vainshtein
mechanism is possible and, thus, some peculiar observational signatures should
be detectable and make it distinguishable from general relativity. We apply
this model to a sample of clusters of galaxies observed under the CLASH survey,
using both new data from gravitational lensing events and archival data from
X-ray intra-cluster hot gas observations. In particular, we use the latter to
model the gas density, and then use it as the only ingredient in the matter
clusters' budget to calculate the expected lensing convergence map. Results
show that, in the context of this extended Galileon, the assumption of having
only gas and no Dark Matter at all in the clusters is able to match
observations. We also obtain narrow and very interesting bounds on the
parameters which characterize this model. In particular, we find that, at least
for one of them, the general relativity limit is excluded at $2\sigma$
confidence level, thus making this model clearly statistically different and
competitive with respect to general relativity.