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.