Quintessence models and the cosmological evolution ofα

The cosmological evolution of a quintessencelike scalar field $\varphi$ coupled to matter and gauge fields leads to effective modifications of the coupling constants and particle masses over time. We analyze a class of models where the scalar field potential $V(\varphi )$ and the couplings to matter $B(\varphi )$ admit common extremum in $\varphi$, as in the Damour-Polyakov ansatz. We find that even for the simplest choices of potentials and $B(\varphi )$, the observational constraints on $\Delta \alpha /\alpha$ coming from quasar absorption spectra, the Oklo phenomenon and Big Bang nucleosynthesis provide complementary constraints on the parameters of the model. We show the evolutionary history of these models in some detail and describe the effects of a varying mass for dark matter.