  In this paper we present a gauge-invariant formalism for perturbations of the
brane-world model developed by the author, A. Ishibashi and O. Seto recently,
and analyze the behavior of cosmological perturbations in a spatially flat
expanding universe realized as a boundary 3-brane in AdS$^5$ in terms of this
formalism. For simplicity we restrict arguments to scalar perturbations. We
show that the behavior of cosmological perturbations on superhorizon scales in
the brane-world model is the same as that in the standard no-extradimension
model, irrespective of the initial condition for bulk perturbations, in the
late stage when the cosmic expansion rate $H$ is smaller than the inverse of
the bulk curvature scale $\ell$. Further, we give rough estimates which
indicate that in the early universe when $H$ is much larger than $1/\ell$,
perturbations in these two models behave quite differently, and the
conservation of the Bardeen parameter does not hold for superhorizon
perturbations in the brane-world model.
