Possible link between the changing fine-structure constant and the accelerating universe via scalar-tensor theory

In 1976, Shlyakhter showed that the Sm data from Oklo results in the upper bound on the time-variability of the fine-structure constant: $\mathrm{\mid }\dot{\alpha }\mathrm{/}\alpha \mathrm{\mid }\text{lsim}{10}^{-17}{\mathrm{y}}^{-1}$, which has ever been the most stringent bound. Since the details have never been published, however, we recently re-analyzed the latest data according to Shlyakhter’s recipe. We nearly re-confirmed his result. To be more precise, however, the Sm data gives either an upper-bound or an “evidence” for a changing $\alpha$: $\dot{\alpha }\mathrm{/}\alpha =-(0.44\pm 0.04)\times {10}^{-16}{\mathrm{y}}^{-1}$. A remark is made to a similar re-analysis due to Damour and Dyson. We also compare our result with a recent “evidence” due to Webb et al, obtained from distant QSO’s. We point out a possible connection between this time-dependence and the behavior of a scalar field supposed to be responsible for the acceleration of the universe, also revealed recently.