  We quantify the slow-roll corrections to primordial density perturbations
arising from inflation driven by a four-dimensional scalar field with a
monomial potential in a five-dimensional non-compact bulk spacetime. Although
the difference between the classical brane-world solutions and standard
four-dimensional solutions is large at early times, the change to the amplitude
at late times of perturbations generated from quantum fluctuations is
first-order in slow-roll parameters, leading to second-order slow-roll
corrections to the spectral index. This confirms that the leading-order effects
are correctly given by previous work in the literature.
