We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass m2 = -2(2ℓ-1)(ℓ+1)H2 and m2 = -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 m2 = 2H2 due to a spin-0 perturbation with m2 = 2H2. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with m2 = 2H2. 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 ω = 3Hrc in the - branch and ω = -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.
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