We show that general infrared modifications of the Einstein-Hilbert action obtained by addition of curvature invariants are not viable. These modifications contain either ghosts or light gravity scalars. A very specific fine-tuning might solve the problem of ghosts, but the resulting theory is still equivalent to a scalar-tensor gravity and thus gives a corrupted picture of gravity at the solar system scale. The only known loophole is that the theory becomes higher dimensional at large distances. The infinite number of degrees of freedom introduced in this way is not reducible to the addition of an arbitrary function of curvature invariants.

7 pages; v2: typos corrected