  We develop a formalism to study non-local higher-dimensional effects in
braneworld scenarios from a four-dimensional effective theory point of view and
check it against the well-known Garriga-Tanaka result in the appropriate limit.
We then use this formalism to study the spectrum of density perturbations
during inflation as seen from the lower-dimensional effective theory. In
particular, we find that the gravitational potential is greatly enhanced at
short wavelengths. The consequences to the curvature perturbations are
nonetheless very weak and will lead to no characteristic signatures on the
power spectrum.
