Behavior of cosmological perturbations in the brane-world model

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 e. Further, we give rough estimates which indicate that in the early universe when H is much larger than 1/l, 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.