Cosmological evolution of Alpha driven by a general coupling with   Quintessence
  A general model for the cosmological evolution of the fine structure constant \alpha driven by a typical Quintessence scenario is presented. We consider a coupling between the Quintessence scalar \phi and the electromagnetic kinetic term F^2, given by a general function B_F(\phi). We study the dependence of the cosmological \Delta\alpha(t) upon the functional form of B_F and discuss the constraints imposed by the data. We find that different cosmological histories for \Delta\alpha(t) are possible within the avaliable constraints. We also find that Quasar absorption spectra evidence for a time variation of alpha, if confirmed, is not incompatible with Oklo and meteorites limits. 
Valerio Marra, Francesca Rosati (Padova)