Constraints on the time variation of the speed of light using Strong lensing.

Due to the recent growth of discoveries of strong gravitational lensing (SGL) systems, one can statistically study both lens properties and cosmological parameters from 161 galactic scale SGL systems. We analyze meVSL model with the velocity dispersion of lenses by adopting the redshift and surface mass density depending power-law mass model. Analysis shows that meVSL models with various dark energy models including $\Lambda$CDM, $\omega$CDM, and CPL provide the negative values of meVSL parameter, $b$ when we put the prior to the $\Omega_{m 0}$ value from Planck. These indicate the faster speed of light and the stronger gravitational force in the past. However, if we adopt the WMAP prior on $\Omega_{m0}$, then we obtain the null results on $b$ within 1-$\sigma$ CL for the different dark energy models.