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 a 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 phi 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(phi) and the couplings to matter B(phi) admit common extremum in phi naturally explains constraints on variations of both the fine structure constant and the proton-electron mass ratio.