  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 $m^2 =
-2(2\ell-1) (\ell +1) H^2$ and $m^2 = -2\ell(2\ell+3) H^2$ where $\ell$ is an
integer. There are two branches ($\pm$ branches) of solutions for the
background spacetime. In the $+$ branch, which includes the self-accelerating
universe, a resonance appears for a mode with $m^2 = 2 H^2$ 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
$m^2 = 2H^2$. 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 van
Dam-Veltman-Zakharov discontinuity in de Sitter spacetime.
  On sufficiently small scales, we confirm that the lineariaed gravity on the
brane is well described by the Brans-Dicke theory with $\omega=3Hr_c$ in $-$
branch and $\omega = -3H r_c$ in $+$ branch, respectively, which confirms the
existence of the ghost in $+$ branch. We also study large scale perturbations.
In $+$ branch, the resonance induces a non-trivial anisotropic stress on the
brane via the projection of Weyl tensor in the bulk, but no instability is
shown to exist on the brane.
