We explore a version of the cosmological dilaton-fixing and decoupling mechanism in which the dilaton dependence of the low-energy effective action is extremized for infinitely large values of the bare string coupling $g_s^2{=e}^{\phi }.$ We study the efficiency with which the dilaton $\phi$ runs away toward its “fixed point” at infinity during a primordial inflationary stage, and thereby approximately decouples from matter. The residual dilaton couplings are found to be related to the amplitude of the density fluctuations generated during inflation. For the simplest inflationary potential $V\left(\chi \right)=\frac{1}{2}{m}_{\chi }^2\left(\phi \right){\chi }^2,$ the residual dilaton couplings are shown to predict violations of the universality of gravitational acceleration near the $\Delta a/a\sim {10}^{-12}$ level. This suggests that a modest improvement in the precision of equivalence principle tests might be able to detect the effect of such a runaway dilaton. Under some assumptions about the coupling of the dilaton to dark matter and/or dark energy, the expected time variation of natural “constants” (in particular of the fine-structure constant) might also be large enough to be within reach of improved experimental or observational data.

• Received 13 May 2002

DOI:https://doi.org/10.1103/PhysRevD.66.046007