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The possible time variation of the fundamental constants of nature has beenan active subject of research since the large-number hypothesis was proposed byDirac. In this paper, we propose a new method to investigate a possible timevariation of the speed of light ($c$) along with the fine-structure constant($\alpha$) using Strong Gravitational Lensing (SGL) and Type Ia Supernovae (SNeIa) observations. We assume a general approach to describe the massdistribution of lens-type galaxies, the one in favor of the power-law indexmodel (PLAW). We also consider the runaway dilaton model to describe a possibletime-variation of $\alpha$. In order to explore the results deeply, we splitthe SGL sample into five sub-samples according to the lens stellar velocitydispersion and three sub-samples according to lens redshift. The resultssuggest that it is reasonable to treat the systems separately, but no strongindication of varying $c$ was found.

journal of cosmology and astroparticle physics

Constraining a possible time-variation of the speed of light along with  the fine-structure constant using strong gravitational lensing and Type Ia  supernovae observations