Revisiting non-Gaussianity of multiple-field inflation from the field equation

Abstract

In the present paper, we study the non-Gaussianity of multiple-field inflation model using the method of the field equation. We start from reviewing the background and the perturbation theory of multiple-field inflation, and then derive the Klein-Gorden equation for the perturbations at second order. Afterward, we calculate the tree-level bispectrum of the fields' perturbations and finally give the corresponding parameter $f_{NL}$ for the curvature perturbation $\zeta$ in virtue of the $\delta N$ formalism. We also compare our result with the one already obtained from the Lagrangian formalism, and find they are consistent. This work may help us understand perturbation theory of inflation more deeply.

arXiv comment19 pages

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• Curvaton with Polynomial Potential
• Primordial Non-Gaussianities of General Multiple Field Inflation
• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part I: the Bispectrum
• Curvaton Dynamics and the Non-Linearity Parameters in Curvaton Model
• $\alpha$-vacuum and inflationary bispectrum
• N-vaton
• Non-Gaussianity, Isocurvature Perturbation, Gravitational Waves and a No-Go Theorem for Isocurvaton
• Spectral Index in Curvaton Scenario
• On Cross-correlations between Curvature and Isocurvature Perturbations during Inflation
• Reconstruction of the isocurvaton scenario
• Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary Models