In this paper, we implement a new method to test the invariance of the speed of light (c) as a function of redshift, by combining the measurements of galaxy cluster gas mass fraction, H(z) from cosmic chronometers, and Type-Ia supernovae (SNe Ia). In our analyses, we consider both a constant depletion factor (which corresponds to the ratio by which the cluster gas mass fraction is depleted with respect to the universal baryonic mean) and one varying with redshift. We also consider the influence of different H 0 estimates on our results. We look for a variation of c, given by c(z) = c 0(1+c 1 z). We find a degeneracy between our final results on c variation and the assumptions on the gas mass fraction depletion factor. Most of our analyses indicate negligible variation of the speed of light.

The Einstein equivalence principle in the electromagnetic sector can be violated in modifications of gravity theory generated by a multiplicative coupling of a scalar field to the electromagnetic Lagrangian. In such theories, deviations of the standard result for the cosmic distance duality relation, and a variation of the fine structure constant are expected and are unequivocally intertwined. In this paper, we search for these possible cosmological signatures by using galaxy cluster gas mass fraction measurements and cosmic chronometers. No significant departure from general relativity is found regardless of our assumptions about cosmic curvature or a possible depletion factor evolution in cluster measurements.