de Sitter limit of inflation and nonlinear perturbation theory

Abstract

We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.

14 pages, 1 figure; typos corrected and discussion of tensor modes added

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• Inflationary tensor fossils in large-scale structure
• Perturbative Quantum Gravity Comes of Age
• Predictions for Nongaussianity from Nonlocal Inflation
• Resonant Trispectrum and a Dozen More Primordial N-point functions
• Inflationary perturbation theory is geometrical optics in phase space
• Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation
• One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics
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• Issues Concerning Loop Corrections to the Primordial Power Spectra
• Path Integral for Inflationary Perturbations
• Transport equations for the inflationary trispectrum
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• Modular Fluctuations in Cosmology
• Generating large primordial fluctuations in single-field inflation for PBH formation
• Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary Models
• A Match Made in Heaven: Linking Observables in Inflationary Cosmology
• On the four-dimensional effective theories in brane-worlds