An excuse for revising a theory of time-varying "constants"

Abstract

In this paper we compare the dimensional method with the Lie groups tactic in order to show the limitations and advantages of each technique. For this purpose we study in detail a perfect fluid cosmological model with time-varying "constants" by using dimensional analysis and the symmetry method. We revise our previous conclusion about the variation of the fine structure constant finding for example that in the radiation predominance era if $\alpha$ varies is only due to the variation of $e^{2}\epsilon_{0}^{-1}$ since $c\hbar=const$ in this era.