DGP Specteroscopy

TL;DR

This work analyzes gravitational perturbations in codimension-1 DGP braneworlds, revealing a 4D ghost on the self-accelerating branch for all brane tensions and a ghost-free normal branch. Through mode expansion, boundary-value analysis, and an effective 4D action, it identifies the ghost as the helicity-0 component of a localized light graviton (or its radion mix) in the self-accelerating background, with a milder tachyonic instability arising from a scalar mode and from Z2-breaking perturbations. The study also demonstrates that non-normalizable bulk modes and nonlocal boundary conditions can induce ghost-like behaviors, challenging the viability of self-acceleration as a gravity-driven explanation for cosmic acceleration. Conversely, the normal branch remains perturbatively ghost-free and offers a robust framework for IR modifications of gravity, while shock-wave analyses highlight IR nonlocalities and their potential implications for brane dynamics.

Abstract

We systematically explore the spectrum of gravitational perturbations in codimension-1 DGP braneworlds, and find a 4D ghost on the self-accelerating branch of solutions. The ghost appears for any value of the brane tension, although depending on the sign of the tension it is either the helicity-0 component of the lightest localized massive tensor of mass $0<m^2 < 2H^2$ for positive tension, the scalar `radion' for negative tension, or their admixture for vanishing tension. Because the ghost is gravitationally coupled to the brane-localized matter, the self-accelerating solutions are not a reliable benchmark for cosmic acceleration driven by gravity modified in the IR. In contrast, the normal branch of solutions is ghost-free, and so these solutions are perturbatively safe at large distance scales. We further find that when the $\mathbb{Z}_2$ orbifold symmetry is broken, new tachyonic instabilities, which are much milder than the ghosts, appear on the self-accelerating branch. Finally, using exact gravitational shock waves we analyze what happens if we relax boundary conditions at infinity. We find that non-normalizable bulk modes, if interpreted as 4D phenomena, may open the door to new ghost-like excitations.