Constraining the minimally extended varying speed of light model using time dilations

The Robertson–Walker (RW) metric, derived from the cosmological principle and Weyl’s postulate, characterizes the ΛCDM cosmological model. Traditionally, in this framework, the assumption of a constant speed of light leads to specific cosmological time dilation (TD). However, because the Robertson–Walker metric lacks a way to define time dilation, the speed of light, like wavelength and temperature, may vary with cosmic time. The minimally extended varying speed of light (meVSL) model fits standard cosmological observations while considering the evolution of physical constants. One model-independent test for the meVSL model is cosmological time dilation. However, current data cannot distinguish between the meVSL model and the standard model.