Filtering gravity: Modification at large distances?

In this lecture I address the issue of possible large distance modi. cation of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions are rather general and apply to large class of theories in which, already at the Newtonian level, gravity changes the regime at a certain very large crossover distance r(c). In such theories the cosmological evolution gets dramatically modified at the crossover scale, usually exhibiting a "self-accelerated" expansion, which can be differentiated from more conventional "dark energy" scenarios by precision cosmology. However, unlike the latter scenarios, theories of modified-gravity are extremely constrained (and potentially testable) by the precision gravitational measurements at much shorter scales. The reason is that modification implies the new propagating light degrees of freedom (additional polarizations of graviton) which penetrate at short distances in a rather profound way, and lead to the deviations from Einstein's gravity at the source-dependent scales, that for the light sources are way below r(c). At the level of the straightforward perturbative expansion in Newtonian coupling, new polarizations exhibit a "strong coupling" behavior, which invalidates the linearized approximation at short distances and is essential for the observational viability of the theory. We clarify some physical aspects of this phenomenon and the role of the resummed solutions.