Strong coupling in brane-induced gravity in five dimensions

TL;DR

The paper analyzes brane-induced gravity in a five-dimensional DGP setup, focusing on linearized and cubic-order dynamics to uncover a fundamental strong-coupling scale. It shows that scalar modes interact strongly above $E_{strong}=ig(M^9/M_{Pl}^4ig)^{1/5}$, implying strong coupling at surprisingly low energies and lengths (below ~30 m for $r_c\sim H_0^{-1}$), thereby challenging the model as a mechanism for cosmic acceleration. Through careful gauge choices and brane-bending redefinitions, leading large terms cancel but residual cubic interactions persist, establishing the scale at which classical treatment fails. The work highlights conceptual and phenomenological tensions in no-ghost brane-worlds with ultra-large-scale gravity modifications and points to the need for further investigation of viable high-dimensional gravity theories.

Abstract

Brane-induced gravity in five dimensions (Dvali--Gabadadze--Porrati model) exhibits modification of gravity at ultra-large distances, $r\gg r_c = M_{Pl}^2/M^3$ where $M$ is the five-dimensional gravity scale. This makes the model potentially interesting for explaining the observed acceleration of the Universe. We argue, however, that it has an intrinsic intermediate energy scale $(M^9/M_{Pl}^4)^{1/5}$. At higher energies, the model is strongly coupled. For $r_c$ of order of the present Hubble size, the strong coupling regime occurs at distanced below tens of metres.