Infrared scaling for a graviton condensate

The universal coupling between gravity and matter dictates a universal scaling for gravity in the infrared in general relativity and in higher curvature theories of gravity. In particular, we will argue that the gravitational fluctuations for a given energy momentum tensor may kick in much before we reach the Planck time and length scale. We will show that the scaling in the infrared is determined by the number of gravitons $N_{g}\gg 1$ and scales like $\ell=\sqrt{N_{g}}\ell_{p}$, where $\ell_p$ is the Planck length. The number, $N_g$, is the occupation number of the gravitons found to be in a displaced vacuum after tracing out the matter degrees of freedom. Furthermore, we will show that gravity is fundamentally different in this regard from the electromagnetic interaction where the number of photons $N_{p}$ scales with the fine structure constant, and there is no infrared scaling in the case of photons.