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.
Watson, Scott and Rham, Claudia De, "Living on a dS Brane: Effects of KK modes on Inflation" (2007). Physics. Paper 411.
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