No need for dark matter in galaxy clusters within Galileon theory
  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 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 \textit{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.
