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The spectrum of cosmological perturbations produced by a multi-component inflaton to second order in the slow-roll approximation

Takahiro T. Nakamura, Ewan D. Stewart

Abstract

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.

The spectrum of cosmological perturbations produced by a multi-component inflaton to second order in the slow-roll approximation

Abstract

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.

Paper Structure

This paper contains 8 sections, 66 equations.

Table of Contents

  1. Introduction
  2. Homogeneous background and slow-roll approximation
  3. Perturbation
  4. Power spectrum and spectral index of $\cal R_{\rm c}$
  5. Summary
  6. Slow-roll conditions
  7. Derivation of Eq.\ref{['9']}
  8. Some useful formulae