Slowly evolving early universe and a phenomenological model for time-dependent fundamental constants and the leptonic masses

A phenomenological model with an extreme accuracy is proposed for the cosmic time variation of the primordial fundamental constants (e, h, G and c) and the leptonic masses. The model is purely exploratory in that at the very early times the light speed is purposely modeled to be negligibly small, indicating a very slowly expanding universe around t=0. The impact of this idea in cosmology and its modeling is overwhelming.