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 universe, 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 crossover 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 $0<{m}^{2}<2{H}^{2}$ and there is a normalizable 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 fluctuation 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 ${m}^{2}=2{H}^{2}$, which coincides with the mass of the brane fluctuation mode. Then 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.