Time Variation of Fine Structure Constant and Proton-Electron Mass Ratio with Quintessence

Recent astrophysical observations of quasar absorption systems indicate that the fine structure constant $\alpha$ and the proton-electron mass ratio $\mu$ may have evolved through the history of the universe. Motivated by these observations, we consider the cosmological evolution of a quintessence-like scalar field $\varphi$ coupled to gauge fields and matter which leads to effective modifications of the coupling constants and particle masses over time. We show that a class of models where the scalar field potential $V(\varphi )$ and the couplings to matter $B(\varphi )$ admit common extremum in $\varphi$ naturally explains constraints on variations of both the fine structure constant and the proton-electron mass ratio.