  We construct a model where cosmological perturbations are analytically solved
based on dilatonic brane worlds. A bulk scalar field has an exponential
potential in the bulk and an exponential coupling to the brane tension. The
bulk scalar field yields a power-law inflation on the brane. The exact
background metric can be found including the back-reaction of the scalar field.
Then exact solutions for cosmological perturbations which properly satisfy the
junction conditions on the brane are derived. These solutions provide us an
interesting model to understand the connection between the behavior of
cosmological perturbations on the brane and the geometry of the bulk. Using
these solutions, the behavior of an anisotropic stress induced on the
inflationary brane by bulk gravitational fields is investigated.
