  We study slow-roll inflation on a three-brane in a five-dimensional bulk
where the effects of energy loss from the brane due to graviton emission is
included in a self-consistent manner. We explicitly derive the form of the
energy loss term due to inflaton-to-graviton scattering and thus determine the
precise dynamics of the two resulting inflationary solutions. What is also
remarkable is that nonconservation of energy on the brane causes the curvature
perturbation to not be conserved on superhorizon scales even for the purely
adiabatic perturbations produced in single-field inflation. Thus the standard
method of calculating the power spectrum of inflaton fluctuations at Hubble
exit and equating it to the power spectrum at horizon reentry no longer holds.
The superhorizon evolution of the perturbations must be tracked from horizon
exit through to when the modes reenter the horizon for the late time power
spectrum to be calculated. We develop the methodology to do this in this paper
as well.
