Are there ghosts in the self-accelerating brane universe?

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 $H{r}_c$, 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 ($H{r}_c>1$), the spin-2 graviton has mass in the range $0<m^2<2H^2$ and there is a normalisable brane fluctuation mode with mass $m^2=2H^2$. 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 $1/2<H{r}_c<1$. This confirms the results obtained by the boundary effective action that there exists a scalar ghost mode for $H{r}_c>1/2$. In a self-accelerating universe $H{r}_c=1$, 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 $H{r}_c=1$, although a careful calculation of the effective action is required to verify this rigorously.

5 pages, 1 figure, significant revisions, conclusion on the self- accelerating universe changed

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