Numerical study of curvature perturbations in a brane-world inflation at high-energies

We study the evolution of scalar curvature perturbations in a brane-world inflation model in a 5D anti-de Sitter space–time. The inflaton perturbations are confined to a 4D brane but they are coupled to the 5D bulk metric perturbations. We numerically solve full coupled equations for the inflaton perturbations and the 5D metric perturbations using the Hawkins–Lidsey inflationary model. At an initial time, we assume that the bulk is unperturbed. We find that the inflaton perturbations at high energies are strongly coupled to the bulk metric perturbations even on subhorizon scales, leading to the suppression of the amplitude of the comoving curvature perturbations at a horizon crossing. This indicates that the linear perturbations of the inflaton field do not obey the usual 4D Klein–Gordon equation due to the coupling to 5D gravitational fields on small scales, and it is necessary to quantize the coupled brane–bulk system in a consistent way in order to calculate the spectrum of the scalar perturbations in a brane-world inflation