  We derive general analytic formulae for the power spectrum and spectral index
of the curvature perturbation produced during inflation driven by a
multi-component inflaton field, up to the second order in the slow-roll
approximation. We do not assume any specific properties of the potential or the
metric on the scalar field space, except for the slow-roll condition, Einstein
gravity, and the absence of any permanent isocurvature modes.
