Ghosts in the self-accelerating universe

TL;DR

The paper analyzes the ghost instability in the self-accelerating DGP braneworld by performing a detailed spectrum analysis of linearized perturbations about a de Sitter brane, identifying the ghost as arising from a mixing between the brane-bending (spin-0) mode and the helicity-0 component of a massive spin-2 KK mode. It shows that on small scales the effective theory resembles Brans-Dicke gravity with parameter ω = -3Hr_c, which yields a ghost when Hr_c > 1/2, and that non-linear interactions (the Vainshtein mechanism) do not remove the ghost in the self-accelerating branch. The authors also cover non-perturbative solutions (Schwarzschild-like and domain-wall configurations) that indicate persistent instabilities in the self-accelerating background. They discuss potential remedies and conclude that simple model modifications do not easily cure the ghost, highlighting the need for UV completions or alternative theories.

Abstract

The self-accelerating universe realizes the accelerated expansion of the universe at late times by large-distance modification of general relativity without a cosmological constant. The Dvali-Gabadadze-Porrati (DGP) braneworld model provides an explicit example of the self-accelerating universe. Recently, the DGP model becomes very popular to study the observational consequences of the modified gravity models as an alternative to dark energy models in GR. However, it has been shown that the self-accelerating universe in the DGP model contains a ghost at the linearized level. The ghost carries negative energy densities and it leads to the instability of the spacetime. In this article, we review the origin of the ghost in the self-accelerating universe and explore the physical implication of the existence of the ghost.

Figures (4)

• Figure 1: Summary of the behaviour of gravity in the DGP model. At large scales $r>r_c$, the theory is 5D. On small scales $r<r_c$, gravity becomes 4D but the linearized theory is described by a Brans-Dicke theory. This affects the large scale structure (LSS) and the Integrated Sachs-Wolfe (ISW) effect and its cross-correlation to LSS. Below the Vainstein radius $r < r_*$, the theory approaches GR. This transition can be probed by weak lensing and cluster abundance as the non-linear dynamics is important for these measures. The solar system tests also provide constraints on the model in the 4D Einstein phase. From KK0.
• Figure 2: Embedding of a de Sitter brane in a flat 5D bulk. The brane world volume is the hyperboloid in the Minkowski bulk. The normal branch corresponds to keeping the interior of the hyperboloid, and its mirror image around the brane. In contrast, for the self-accelerating branch, we keep the exterior, and its reflection. From Cha.
• Figure 3: Summary of the mass spectrum of the scalar perturbations in $+$ branch. Spin-2 perturbation has continuous modes with $m^2 \geq (9/4)H^2$ and a discrete mode with $m^2 = m_d^2$ while spin-0 perturbation has $m^2 = 2H^2$. In the limit $Hr_c \to 1$, both the helicity-0 excitation of spin-2 perturbation and the spin-0 perturbation have mass $m^2 = 2H^2$ and there is a resonance.
• Figure 4: Summary of the existence of the ghost. From KK1.