  Modifications of gravity generated by a multiplicative coupling of a scalar
field to the electromagnetic Lagrangian lead to a breaking of Einstein
equivalence principle (EEPB) as well as to variations of fundamental constants.
In these theoretical frameworks, deviations of standard values of the fine
structure constant, $\Delta \alpha/\alpha=\phi$, and of the cosmic distance
duality relation, $D_L(1+z)^{-2}/D_A=\eta=1$, where $D_L$ and $D_A$ are the
luminosity and angular diameter distances, respectively, are unequivocally
linked. In this paper, we search for cosmological signatures of the EEPB by
using angular diameter distance from galaxy clusters, obtained via their
Sunyaev-Zeldovich effect (SZE) and X-ray observations, and distance modulus of
type Ia supernovae (SNe Ia). The crucial point here is that we take into
account the dependence of the SZE/X-ray technique with $\phi$ and $\eta$. Our
new results show no indication of the EEPB.
