Lower Limit to the Scale of an Effective Theory of Gravitation

We consider a linearized, effective quantum theory of gravitation in which gravity weakens at energies higher than ~10^-3 eV in order to accommodate the apparent smallness of the cosmological constant. Such a theory predicts departures from the static Newtonian inverse-square force law on distances below ~0.05 mm. However, we show that such a modification also leads to changes in the long-range behavior of gravity and is inconsistent with observed gravitational lenses.