Lower Limit to the Scale of an Effective Quantum Theory of Gravitation

An effective quantum theory of gravitation in which gravity weakens at energies higher than $\sim {10}^{-3}\mathrm{eV}$ is one way to accommodate the apparent smallness of the cosmological constant. Such a theory predicts departures from the Newtonian inverse-square force law on distances below $\sim 0.05\mathrm{mm}$. However, it is shown that this modification also leads to changes in the long-range behavior of gravity and is inconsistent with observed gravitational lenses.

Figure 1

(a) The Feynman diagram for the gravitational deflection of light. (b) The leading ladder and crossed-ladder Feynman diagrams for graviton exchange are shown.