Classical and Quantum Consistency of the DGP Model
Alberto Nicolis, Riccardo Rattazzi
TL;DR
This work analyzes the classical and quantum consistency of the DGP model by focusing on the boundary effective action for the brane bending mode π. The authors demonstrate that the cubic π interaction captures the essential non-linear dynamics, including the Vainshtein mechanism that recovers GR in appropriate regimes, and establish classical stability for a broad class of sources while confirming a ghost in the self-accelerating de Sitter branch. Quantum corrections threaten predictivity unless UV counterterms are constrained so that a local running scale \\tilde{Λ}(x) governed by the extrinsic curvature controls the dynamics, effectively treating K_{μν} as a dilaton. The framework shows that, with the proposed counterterm structure, the model remains calculable and phenomenologically viable in astrophysical contexts, though the de Sitter ghost pose a fundamental caveat for the self-accelerating solution. Overall, the paper provides a careful, sector-by-sector assessment of stability and quantum consistency, offering a path to a UV-complete, calculable DGP-like theory with controlled predictivity at macroscopic scales.
Abstract
We study the Dvali-Gabadadze-Porrati model by the method of the boundary effective action. The truncation of this action to the bending mode πconsistently describes physics in a wide range of regimes both at the classical and at the quantum level. The Vainshtein effect, which restores agreement with precise tests of general relativity, follows straightforwardly. We give a simple and general proof of stability, i.e. absence of ghosts in the fluctuations, valid for most of the relevant cases, like for instance the spherical source in asymptotically flat space. However we confirm that around certain interesting self-accelerating cosmological solutions there is a ghost. We consider the issue of quantum corrections. Around flat space πbecomes strongly coupled below a macroscopic length of 1000 km, thus impairing the predictivity of the model. Indeed the tower of higher dimensional operators which is expected by a generic UV completion of the model limits predictivity at even larger length scales. We outline a non-generic but consistent choice of counterterms for which this disaster does not happen and for which the model remains calculable and successful in all the astrophysical situations of interest. By this choice, the extrinsic curvature K_{μν} acts roughly like a dilaton field controlling the strength of the interaction and the cut-off scale at each space-time point. At the surface of Earth the cutoff is \sim 1 cm but it is unlikely that the associated quantum effects be observable in table top experiments.