Consistency testing for invariance of the speed of light at different
  redshifts: the newest results from strong lensing and type Ia supernovae
  observations
  The invariance of the speed of light in the distant universe has profound
significance for fundamental physics. In this paper, we propose a new
model-independent method to test the invariance of the speed of light $c$ at
different redshifts by combining the strong gravitational lensing (SGL) systems
and the observations of type-Ia supernovae (SNe Ia). All the quantities used to
test the deviation of $c$ come from the direct observations, and the absolute
magnitudes of SNe Ia need not to be calibrated. Our results show that the speed
of light in the distant universe is no obvious deviation from the constant
value $c_0$ within the uncertainty based on current observations. Moreover, we
conclude that the currently compiled SGL and SNe Ia Pantheon samples may
achieve much higher precision $\Delta c/c\sim10^{-2}$ for the deviation of $c$
than all previously considered approaches. The forthcoming data from the Legacy
Survey of Space and Time and Wide-Field InfraRed Space Telescope will achieve
more stringent testing for deviation of the SOL (at the level of $\Delta c/c
\sim10^{-3}$) by using our model-independent method. Finally, we discuss the
potential ways in which our technique might be improved, focusing on the
treatment of possible sources of systematic uncertainties.
