Astrophysical constraints on modifying gravity at large distances

Recently, several interesting proposals were made modifying the law of gravity on large scales, within a sensible relativistic formulation. This allows a precise formulation of the idea that such a modification might account for galaxy rotation curves, instead of the usual interpretation of these curves as evidence for dark matter. Here we summarize several observational constraints that any such modification must satisfy, and which we believe make more challenging, any interpretation of galaxy rotation curves in terms of new gravitational physics.