(De)coupling Limit of DGP

TL;DR

This paper analyzes the decoupling limit of the DGP gravity model, revealing that it retains tensor-scalar interactions unlike simpler scalar models, affecting the interpretation of superluminality and positivity constraints.

Contribution

It demonstrates that the DGP decoupling limit includes tensor-scalar mixing, contrasting with scalar sigma models, and clarifies implications for superluminality and positivity bounds.

Findings

The decoupling limit does not reduce to a pure scalar sigma model.

Static spherically symmetric solutions differ from scalar model predictions.

Long-range tensor interactions invalidate certain positivity bounds.

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.