The power spectrum for a multi-component inflaton to second-order corrections in the slow-roll expansion

We derive the power spectrum P(k) of the density perturbations produced during inflation up to second-order corrections in the standard slow-roll approximation for an inflaton with more than one degree of freedom. We also present the spectral index n up to first-order corrections including previously missing terms, and the running dn/d Ink to leading order. (C) 2002 Published by Elsevier Science B.V.