  We investigate the scalar metric perturbations about a de Sitter brane
universe in a 5-dimensional anti de Sitter bulk. We compare the master-variable
formalism, describing metric perturbations in a 5-dimensional longitudinal
gauge, with results in a Gaussian normal gauge. For a vacuum brane (with
constant brane tension) there is a continuum of normalizable Kaluza-Klein
modes, with m>3H/2, which remain in the vacuum state. A light radion mode, with
m=\sqrt{2}H, satisfies the boundary conditions for two branes but is not
normalizable in the single-brane case. When matter is introduced (as a test
field) on the brane, this mode, together with the zero-mode and an infinite
ladder of discrete tachyonic modes, become normalizable. However, the boundary
condition requires the self-consistent 4-dimensional evolution of scalar field
perturbations on the brane and the dangerous growing modes are not excited.
These normalizable discrete modes introduce corrections at first-order to the
scalar field perturbations computed in a slow-roll expansion. On super-Hubble
scales, the correction is smaller than slow-roll corrections to the de Sitter
background. However on small scales the corrections can become significant.
