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.