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.
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