Probing variation of the fine-structure constant in runaway dilaton models using Strong Gravitational Lensing and Type Ia Supernovae

In order to probe a possible time variation of the fine-structure constant ($alpha$), we propose a new method based on Strong Gravitational Lensing and Type Ia Supernovae observations. By considering a class of dilaton runaway models, where $frac{Delta alpha}{alpha}= - gamma ln{(1+z)}$, we obtain constraints on $frac{Delta alpha}{alpha}$ at the level $gamma approx 10^{-2}$ ($gamma$ captures the physical properties of the model). Since the data set covers the redshift range $0.075 leq z leq 2.2649$, the constraints derived here provide independent bounds on a possible time variation of $alpha$ at low, intermediate and high redshifts.