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

TL;DR

This paper compares dimensional analysis and Lie group methods to analyze a cosmological model with time-varying constants, revising previous conclusions about the fine structure constant's variation in different cosmic eras.

Contribution

It demonstrates the strengths and limitations of dimensional and symmetry methods in studying models with varying physical constants, providing new insights into their applicability.

Findings

In the radiation era, the variation of the fine structure constant is due to changes in e^2/ε_0.

The condition cħ=const influences the variation of constants.

Comparison clarifies the use of different analytical techniques in cosmological models.

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.