Are there ghosts in the self-accelerating brane universe?

We study gravitational perturbations about a de Sitter brane with the induced 4D Einstein-Hilbert term, in a 5D Minkowski spacetime. 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. We show that in the self-accelerating brane universe without matter fields, the spin-2 graviton has mass $m^2=2H^2$ and there are no helicity-0 excitations, due to the existence of a symmetry for perturbations, which is the same gauge symmetry as in the 4D Pauli-Fierz massive gravity theory with mass $M^2=2H^2$. If we introduce a cosmological constant on the brane, the symmetry breaks down. Then there arises a spin-0 perturbation sourced by the fluctuation of the brane and the spin-2 graviton has mass in the range $0 < m^2 < 2H^2$. Although the spin-0 perturbation is healthy, the spin-2 graviton acquires a helicity-0 excitation that is a ghost. This implies that the de Sitter brane with a true cosmological constant is unstable while the self-accelerating brane universe is stable. This may provide a new way to explain the vanishing of the cosmological constant.