Varying Fine-Structure Constant and the Cosmological Constant Problem

We start with a brief account of the latest analysis of the Oklo phenomenon providing the still most stringent constraint on time variability of the fine-structure constant α. Comparing this with the recent result from the measurement of distant QSO's appears to indicate a non-uniform time-dependence, which we argue to be related to another recent finding of the accelerating universe. This view is implemented in terms of the scalar-tensor theory, applied specifically to the small but nonzero cosmological constant. Our detailed calculation shows that these two phenomena can be understood in terms of a common origin, a particular behavior of the scalar field, dilaton. We also sketch how this theoretical approach makes it appropriate to revisit non-Newtonian gravity featuring small violation of Weak Equivalence Principle at medium distances. This revised version was published online in July 2006 with corrections to the Cover Date.