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

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