Modifications of gravity generated by a multiplicative coupling of a scalar field to the electromagnetic Lagrangian lead to a breaking of the 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, $\mathrm{\Delta }\alpha /\alpha =\varphi$, 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-Zel’dovich 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 $\varphi$ and $\eta$. Our new results show no indication of the EEPB.

• Received 10 May 2016

DOI:https://doi.org/10.1103/PhysRevD.94.023524