THE SPECTRUM OF COSMOLOGICAL PERTURBATIONS PRODUCED BY A MULTICOMPONENT INFLATON TO 2ND-ORDER IN THE SLOW-ROLL APPROXIMATION

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