Time Variation of the Fine Structure Constant Driven by Quintessence

There are indications from the study of quasar absorption spectra that the fine structure constant $\alpha$ may have been measurably smaller for redshifts $z>2.$ Analyses of other data (${}^{149}$Sm fission rate for the Oklo natural reactor, variation of ${}^{187}$Re $\beta$-decay rate in meteorite studies, atomic clock measurements) which probe variations of $\alpha$ in the more recent past imply much smaller deviations from its present value. In this work we tie the variation of $\alpha$ to the evolution of the quintessence field proposed by Albrecht and Skordis, and show that agreement with all these data, as well as consistency with WMAP observations, can be achieved for a range of parameters. Some definite predictions follow for upcoming space missions searching for violations of the equivalence principle.