(De)coupling Limit of DGP

TL;DR

This work examines the decoupling limit of the DGP model, showing that it does not reduce to a purely scalar theory but retains nonlinear mixing with a tensor through extended field equations. By formulating the model in ADM variables and taking a careful decoupling limit, the authors derive a scalar-tensor system with additional nonlinear constraints, demonstrating that scalar-only solutions (e.g., those from pure scalar models) need not solve the full DGP equations. The analysis highlights a consistent Schwarzschild-like solution that exhibits gravitational mass screening and clarifies the differences from 4D massive gravity, including the absence of hidden superluminality in the DGP context. The results indicate that long-range tensor interactions persist in the decoupling limit, complicating analyticity-based positivity bounds and informing the interpretation of DGP phenomenology and its UV completion prospects.

Abstract

We investigate the decoupling limit in the DGP model of gravity by studying its nonlinear equations of motion. We show that, unlike 4D massive gravity, the limiting theory does not reduce to a sigma model of a single scalar field: Non-linear mixing terms of the scalar with a tensor also survive. Because of these terms physics of DGP is different from that of the scalar sigma model. We show that the static spherically-symmetric solution of the scalar model found in hep-th/0404159, is not a solution of the full set of nonlinear equations. As a consequence of this, the interesting result on hidden superluminality uncovered recently in the scalar model in hep-th/0602178, is not applicable to the DGP model of gravity. While the sigma model violates positivity constraints imposed by analyticity and the Froissart bound, the latter cannot be applied here because of the long-range tensor interactions that survive in the decoupling limit. We discuss further the properties of the Schwarzschild solution that exhibits the gravitational mass-screening phenomenon.