Ghost constraints on modified gravity

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.