Are there ghosts in the self-accelerating brane universe?

TL;DR

The paper analyzes gravitational perturbations about a vacuum de Sitter brane in the DGP model, focusing on the self-accelerating branch without a brane cosmological constant. By constructing the boundary effective action and 4D effective actions for discrete spin-2 and helicity-0 modes via a master-variable formulation, it shows that a ghost arises in the spin-2 sector when $H r_c > 1$ and that brane-bending coupling can also generate a ghost, with the special self-accelerating point $H r_c = 1$ likely unstable due to mixing. These findings challenge the viability of a self-accelerating DGP universe and motivate a rigorous, full effective-action verification. The work clarifies the spectrum structure, including discrete and KK modes, and connects to the Higuchi bound through the helicity-0 dynamics of massive gravitons in de Sitter space.

Abstract

We study the spectrum of gravitational perturbations about a vacuum de Sitter brane with the induced 4D Einstein-Hilbert term, in a 5D Minkowski spacetime (DGP model). We consider solutions that include a self-accelerating univese, where the accelerating expansion of the universe is realized without introducing a cosmological constant on the brane. The mass of the discrete mode for the spin-2 graviton is calculated for various $Hr_c$, where $H$ is the Hubble parameter and $r_c$ is the cross-over scale determined by the ratio between the 5D Newton constant and the 4D Newton constant. We show that, if we introduce a positive cosmological constant on the brane ($Hr_c >1$), the spin-2 graviton has mass in the range $0 < m^2 < 2H^2$ and there is a normalisable brane fluctuation mode with mass $m^2=2 H^2$. Although the brane fluctuation mode is healthy, the spin-2 graviton has a helicity-0 excitation that is a ghost. If we allow a negative cosmological constant on the brane, the brane bending mode becomes a ghost for $1/2 < Hr_c <1$. This confirms the results obtained by the boundary effective action that there exists a scalar ghost mode for $Hr_c >1/2$. In a self-accelerating universe $Hr_c=1$, the spin-2 graviton has mass $m^2=2H^2$, which is known to be a special case for massive gravitons in de Sitter spacetime where the graviton has no helicity-0 excitation and so no ghost. However, in DGP model, there exists a brane fluctuation mode with the same mass and there arises a mixing between the brane fluctuation mode and the spin-2 graviton. We argue that this mixing presumably gives a ghost in the self-accelerating universe by continuity across $Hr_c=1$, although a careful calculation of the effective action is required to verify this rigorously.

Figures (1)

• Figure 1: Summary of the existence of the scalar ghost for various $Hr_c$