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 $\frac{\mathrm{\Delta }\alpha }{\alpha }=-\gamma \ln (1+z)$, we obtain constraints on $\frac{\mathrm{\Delta }\alpha }{\alpha }$ at the level $\gamma \approx 10^{-2}$($\gamma$ captures the physical properties of the model). Since the data set covers the redshift range $0.075\le z\le 2.2649$, the constraints derived here provide independent bounds on a possible time variation of $\alpha$ at low, intermediate and high redshifts.