Short distance non-perturbative effects of large distance modified gravity

TL;DR

The paper analyzes a DGP-based large-distance modification of gravity by contrasting the perturbative Schwarzschild (PS) solution with a non-perturbative Schwarzschild (NPS) solution. It shows that nonperturbative effects introduce nonanalytic corrections and a nonzero curvature $R$ extending to the Vainshtein scale $r_*$, leading to subtle but potentially observable modifications to solar-system precession and a mild violation of universal scaling. At $r \ll r_*$ the short-distance potential remains nearly Newtonian with a small nonanalytic correction, while at $r \gg r_*$ PS and NPS diverge in their asymptotics, including mass screening and, for the selfaccelerated branch, a de Sitter-like term and a 5D-like tail. The results highlight how nonperturbative dynamics can influence local gravity tests and motivate further nonlinear and structure-formation studies, as well as considerations of UV completion and strong coupling in brane-induced gravity.

Abstract

In a model of large distance modified gravity we compare the nonperturbative Schwarzschild solution of hep-th/0407049 to approximate solutions obtained previously. In the regions where there is a good qualitative agreement between the two, the nonperturbative solution yields effects that could have observational significance. These effects reduce, by a factor of a few, the predictions for the additional precession of the orbits in the Solar system, still rendering them in an observationally interesting range. The very same effects lead to a mild anomalous scaling of the additional scale-invariant precession rate found by Lue and Starkman.