Testing the speed of light over cosmological distances: the combination
  of strongly lensed and unlensed supernova Ia
  Probing the speed of light is as an important test of General Relativity but
the measurements of $c$ using objects in the distant universe have been almost
completely unexplored. In this letter, we propose an idea to use the multiple
measurements of galactic-scale strong gravitational lensing systems with type
Ia supernova acting as background sources to estimate the speed of light. This
provides an original method to measure the speed of light using objects located
at different redshifts which emitted their light in a distant past. Moreover,
we predict that strongly lensed SNe Ia observed by the LSST would produce
robust constraints on $\Delta c/c$ at the level of $10^{-3}$. We also discuss
whether the future surveys such as LSST may succeed in detecting any
hypothetical variation of $c$ predicted by theories in which fundamental
constants have dynamical nature.
