Limits on evolution of the fine-structure constant in runaway dilaton models from Sunyaev-Zeldovich Observations

In this paper, new bounds on possible variations of the fine structure constant, $\alpha$, for a class of runaway dilaton models are performed. By considering a possible evolution with redshift, $z$, such as $\frac{\Delta\alpha}{\alpha}=-\gamma\ln(1+z)$, where in $\gamma$ are the physical properties of the model, we constrain this parameter by using a deformed cosmic distance duality relation jointly with gas mass fraction (GMF) measurements of galaxy clusters and luminosity distances of type Ia supernovae. The GMF's used in our analyses are from cluster mass data from 82 galaxy clusters in the redshift range $0.12Atacama Cosmology Telescope. The type Ia supernovae are from the Union2.1 compilation. We also explore the dependence of the results from four models used to describe the galaxy clusters. As a result no evidence of variation was obtained.