Strong Interactions and Stability in the DGP Model

TL;DR

This paper analyzes the DGP model's strong interactions and stability issues, revealing a fundamental scale where predictivity is lost and exploring the role of Goldstone modes and background curvature effects.

Contribution

It identifies the strong interaction scale in the DGP model and examines the implications for stability and predictivity, including the role of Goldstone modes and background curvature.

Findings

Strong interactions occur at a scale ~ ( ext{Hubble length})^{2/3} km.

Predictivity is lost at distances shorter than ~ 1000 km if _{DGP} is the Hubble length.

A negative-energy classical solution can be avoided by cutoff at the strong interaction scale.

Abstract

The model of Dvali, Gabadadze, and Porrati (DGP) gives a simple geometrical setup in which gravity becomes 5-dimensional at distances larger than a length scale \lambda_{DGP}. We show that this theory has strong interactions at a length scale \lambda_3 ~ (\lambda_{DGP}^2 / M_P)^{1/3}. If \lambda_{DGP} is of order the Hubble length, then the theory loses predictivity at distances shorter than \lambda_3 ~ 1000 km. The strong interaction can be viewed as arising from a longitudinal `eaten Goldstone' mode that gets a small kinetic term only from mixing with transverse graviton polarizations, analogous to the case of massive gravity. We also present a negative-energy classical solution, which can be avoided by cutting off the theory at the same scale scale \lambda_3. Finally, we examine the dynamics of the longitudinal Goldstone mode when the background geometry is curved.