Predictive power of strong coupling in theories with large distance modified gravity

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 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.