Varying Fine-Structure Constant and the Cosmological Constant Problem1

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. 1. Constraint from Oklo Around 1974 it was finally agreed that self-sustained fission reactions took place naturally in Oklo, Gabon, some 2 billion years ago. This is the “Oklo phenomenon.” Shlyakhter [1] came to notice that measuring isotopic ratio of Sm left in the remnants of the “natural reactors” is useful to determine how much nuclear phenomena 2 billion years ago could have been different from what they are. He focused on the reaction n +Sm → Sm + γ, which is unique in that it is dominated by a resonance lying as low as 97.3 meV, nearly 7 orders of magnitude too small compared with MeV, a typical energy scale of nuclear physics. A very small number like this should be due to a nearly complete cancellation between two large effects; a repulsive Coulomb force proportional to α and the attractive nuclear force. The resonance shows up as a sharp peak in the cross section plotted against a possible change ∆Er of the resonance energy Er. We also assume thermal equilibrium of the neutron flux. Even a slight change of α may result in the sizable change of Er then of the cross section. Thanks to this amplification mechanism, he derived the upper bound; |α̇/α|< ∼10y, much better than any other results for years. Unfortunately, details of his derivation and the quality of the data have been left largely unknown. However, our recent re-analysis [2] shows that his “champion result” itself can be trusted reasonably well. To minimize the “contamination” due to the inflow from outside the reactor that occurred after the end of reactor activity, we relied on the latest samples collected carefully from deep underground. By analyzing the data on the isotopes of Sm, we computed the cross section σ̂149 = (91 ± 6)kb, as bounded by the two horizontal lines in Fig. 1. Combining this with the shaded area corresponding to the improved estimate of the temperature (200− 400)◦C, we Delivered at JENAM 2002, Porto, Portugal, 2-7 September 2002, to be published in Proceedings. E-mail: [email protected]