Improved constraints on violations of the Einstein equivalence principle
  in the electromagnetic sector with complementary cosmic probes
  Recent results have shown that a field non-minimally coupled to the
electromagnetic Lagrangian can induce a violation of the Einstein equivalence
principle. { This kind of coupling is present in a very wide class of
gravitation theories.} In a cosmological context, this would break the validity
of the cosmic distance duality relation as well as cause a time variation of
the fine structure constant. Here, we improve constraints on this scenario by
using four different observables: the luminosity distance of type Ia
supernovae, the angular diameter distance of galaxy clusters, the gas mass
fraction of galaxy clusters and the temperature of the cosmic microwave
background at different redshifts. We consider four standard parametrizations
adopted in the literature and show that, due to a high complementarity of the
data, the errors are shrunk between 20\% and 40\% depending on the
parametrization. We also show that our constraints are weakly affected by the
geometry considered to describe the galaxy clusters. In short, no violation of
the Einstein equivalence principle is detected up to redshifts $\sim$ 3.
