Gravitational lens time delay as a probe of a possible time variation of the fine-structure constant.

A new method based on large scale structure observations is proposed to probe a possible time variation of the fine-structure constant ($\alpha$). Our analysis is mainly based on time-delay of Strong Gravitational Lensing and Type Ia Supernovae observations. By considering a specific class of string theory inspired models called runaway dilaton, where the cosmological evolution of the fine structure constant is given by $\frac{\Delta \alpha}{\alpha} \approx -\gamma \ln{(1+z)}$, we obtain limits on the physical properties parameter of the model ($\gamma$) at the level $10^{-2}$ ($1\sigma$). Although our limits are less restrictive than those obtained by quasar spectroscopy, the approach presented here provides new bounds on a possibility of $\frac{\Delta \alpha}{\alpha} \neq 0$ at a different range of redshifts.