Predictive Power of Strong Coupling in Theories with Large Distance Modified Gravity

TL;DR

This paper argues that any ghost-free large-distance modification of gravity must exhibit a strong coupling phenomenon. It shows that an extra scalar polarization associated with the massive graviton leads to linear vDVZ-like effects, but non-linear self-interactions render these effects non-perturbative below a source-dependent scale $r_*$, making gravity predictions highly testable near gravitating sources. The analysis collapses the class of theories to a one-parameter family $m^2(\square) \simeq r_c^{2(\alpha-1)}\,\square^{\alpha}$ with $\alpha \ge 0$, and derives a universal scaling for the strong-coupling radius $r_*$ and the ensuing corrections to the metric, including perihelion shifts and Lunar Ranging constraints. The framework thus provides a concrete, testable parametrization of large-distance modified gravity and clarifies the interplay between cosmological modification and solar-system tests, while highlighting non-perturbative issues in cosmological backgrounds.

Abstract

We consider theories that modify gravity at cosmological distances, and show that any such theory must exhibit a strong coupling phenomenon, or else it is either inconsistent or is already ruled out by the solar system observations. We show that all the ghost-free theories that modify dynamics of spin-2 graviton on asymptotically flat backgrounds, automatically have this property. Due to the strong coupling effect, modification of the gravitational force is source-dependent, and for lighter sources sets in at shorter distances. This universal feature makes modified gravity theories predictive and potentially testable not only by cosmological observations, but also by precision gravitational measurements at scales much shorter than the current cosmological horizon. We give a simple parametrization of consistent large distance modified gravity theories and their predicted deviations from the Einsteinian metric near the gravitating sources.