DGP Specteroscopy

TL;DR

This paper investigates gravitational perturbations in DGP braneworlds, revealing a ghost instability in the self-accelerating branch and analyzing the stability of solutions and boundary effects.

Contribution

It systematically explores the spectrum of perturbations in DGP models, identifying ghost instabilities and stability conditions for different branches and boundary scenarios.

Findings

Ghost appears on self-accelerating branch regardless of brane tension.

Normal branch solutions are free of ghosts and perturbatively stable.

Breaking orbifold symmetry introduces milder tachyonic instabilities.

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.