  In this work we will test an alternative model of gravity belonging to the
large family of galileon models. It is characterized by an intrinsic breaking
of the Vainshtein mechanism inside large astrophysical objects, thus having
possibly detectable observational signatures. We will compare theoretical
predictions from this model with the observed total mass profile for a sample
of clusters of galaxies. The profiles are derived using two complementary
tools: X-ray hot intra-cluster gas dynamics, and strong and weak gravitational
lensing. We find that a dependence with the dynamical internal status of each
cluster is possible; for those clusters which are very close to be relaxed, and
thus less perturbed by possible astrophysical local processes, the galileon
model gives a quite good fit to both X-ray and lensing observations. Both
masses and concentrations for the dark matter halos are consistent with earlier
results found in numerical simulations and in the literature, and no compelling
statistical evidence for a deviation from general relativity is detectable from
the present observational state. Actually, the characteristic galileon
parameter $\Upsilon$ is always consistent with zero, and only an upper limit
($\lesssim0.086$ at $1\sigma$, $\lesssim0.16$ at $2\sigma$, and $\lesssim0.23$
at $3\sigma$) can be established. Some interesting distinctive deviations might
be operative, but the statistical validity of the results is far from strong,
and better data would be needed in order to either confirm or reject a
potential tension with general relativity.
