We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an in flaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass m(2) = -2(2l - 1)(l + 1) H-2 and m(2) = -2l(2l + 3) H-2 where l is an integer. There are two branches (+/- branches) of solutions for the background spacetime. In the + branch, which includes the self-accelerating universe, a resonance appears for a mode with m(2) = 2H(2) due to a spin-0 perturbation with m(2) = 2H(2). The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with m2 = 2H(2). In the + branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of the van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the linearized gravity on the brane is well described by the Brans-Dicke theory with w = 3Hrc in the - branch and. = - 3Hrc in the + branch, respectively, which confirms the existence of the ghost in the + branch. We also study large scale perturbations. In the + branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of the Weyl tensor in the bulk, but no instability is shown to exist on the brane.
