Slow-roll corrections to inflaton fluctuations on a brane

Quantum fluctuations of an inflaton field, slow rolling during inflation are coupled to metric fluctuations. In conventional four-dimensional cosmology one can calculate the effect of scalar metric perturbations as slowroll corrections to the evolution of a massless free field in de Sitter spacetime. This gives the well-known first-order corrections to the field perturbations after horizon exit. If inflaton fluctuations on a four-dimensional brane embedded in a five-dimensional bulk spacetime are studied to first order in slow roll, then we recover the usual conserved curvature perturbation on superhorizon scales. But on small scales, at high energies, we find that the coupling to the bulk metric perturbations cannot be neglected, leading to a modified amplitude of vacuum oscillations on small scales. This is a large effect which casts doubt on the reliability of the usual calculation of inflaton fluctuations on the brane neglecting their gravitational coupling.