A dynamical systems approach to studying the equivalence principle in dilaton gravity

TL;DR

This paper uses dynamical systems methods to analyze how cosmological evolution in dilaton gravity models influences deviations from the equivalence principle, highlighting a global relaxation mechanism that reduces fifth-force effects over time.

Contribution

It introduces a phase-space approach to connect cosmological dynamics with weak-field deviations in dilaton gravity, emphasizing a global relaxation process distinct from screening mechanisms.

Findings

Stable fixed point associated with minimal coupling is approached asymptotically.

Finite-epoch displacement from the fixed point determines fifth-force effects.

Damping rate of deviations is linked to eigenvalues of the fixed point's Jacobian.

Abstract

We study a string-inspired dilaton cosmology in the Damour--Polyakov (DP) regime using dynamical-systems methods, aiming to make explicit how cosmological relaxation controls deviations from the equivalence principle. Working in the Einstein frame, we consider a spatially flat FLRW universe filled with pressureless matter and a universally coupled dilaton. Expanding the conformal coupling function and the scalar potential around the least-coupling point, we obtain a closed and self-consistent autonomous system governing the late-time evolution of the scalar-matter sector. The resulting phase space contains a stable fixed point associated with least coupling, approached only asymptotically along cosmological trajectories. Therefore, at any finite epoch the solution typically retains a small displacement from the fixed point. In the DP regime this finite-epoch displacement sets the ambient coupling, and thus determines the magnitude of fifth-force effects and deviations from the equivalence principle in the nonrelativistic limit. By linearising the system around a finite-epoch reference state, we show that the damping of the displacement is controlled by the Jacobian eigenvalues of the DP fixed point. This yields a direct dynamical estimate of how rapidly deviations from the equivalence principle are reduced during cosmological evolution. The mechanism is global and cosmological in origin, and is conceptually distinct from local environmental screening as in chameleon or symmetron scenarios. Overall, our results illustrate how phase-space techniques provide a clear bridge between cosmological dynamics and weak-field departures from General Relativity.