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Violations of the equivalence principle in a dilaton-runaway scenario

T. Damour, F. Piazza, G. Veneziano

Abstract

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 $g_s^2 = e^φ$. We study the efficiency with which the dilaton $φ$ runs away towards 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, $V (χ) = {1/2} m_χ^2 (φ) χ^2$, the residual dilaton couplings are shown to predict violations of the universality of gravitational acceleration near the $Δa / a \sim 10^{-12}$ 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.

Violations of the equivalence principle in a dilaton-runaway scenario

Abstract

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 . We study the efficiency with which the dilaton runs away towards 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, , the residual dilaton couplings are shown to predict violations of the universality of gravitational acceleration near the 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.

Paper Structure

This paper contains 11 sections, 86 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Dilaton runaway
  3. The inflationary period
  4. Attraction of $\varphi$ by the subsequent cosmological evolution
  5. Deviations from general relativity induced by a runaway dilaton
  6. Composition-independent deviations from general relativity
  7. Composition-dependent deviations from general relativity
  8. Cosmological variation of "constants"
  9. Spatio-temporal fluctuations of the "constants"
  10. Summary and conclusion
  11. The stochastic evolution of the dilaton

Figures (1)

  • Figure 1: The phase space of the system is represented in the case of a power--law potential (\ref{['eq2.10']}) with $n=2$, $b_\lambda = 0.1$ and $\lambda_\infty = 10^{-10}$. The thick--dashed (red) curves delimitate the quantum behaviour of the two fields, the horizontal curve $\chi = \lambda_\infty^{-1/(n+2)}$ and the hyperbola-like curve $\chi = b_\lambda^{2/n} \lambda_\infty^{-1/n} e^{-2 c\varphi/n}$ being the limit of the quantum behaviour for $\chi$ and $\varphi$ respectively. In the white region both fields have a classical behaviour. The last "fully classical" trajectory has been represented by a thick (blue) curve. The bright--gray regions are those where either the $\varphi$ or the $\chi$ evolution are dominated by quantum fluctuations. The fully--quantum region is the dark--gray region on the top right.