The structure of correlation functions in single field inflation

Abstract

Many statistics available to constrain non-Gaussianity from inflation are simplest to use under the assumption that the curvature correlation functions are hierarchical. That is, if the n-point function is proportional to the (n-1) power of the two-point function amplitude and the fluctuations are small, the probability distribution can be approximated by expanding around a Gaussian in moments. However, single-field inflation with higher derivative interactions has a second small number, the sound speed, that appears in the problem when non-Gaussianity is significant and changes the scaling of correlation functions. Here we examine the structure of correlation functions in the most general single scalar field action with higher derivatives, formalizing the conditions under which the fluctuations can be expanded around a Gaussian distribution. We comment about the special case of the Dirac-Born-Infeld action.

21 Pages, fixed typo in arXiv title; added reference

References in corpus (24)

• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Effective Field Theory for Inflation
• Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?
• Effects of Scale-Dependent Non-Gaussianity on Cosmological Structures
• Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation
• The Inflationary Trispectrum for Models with Large Non-Gaussianities
• Non-Gaussianities in New Ekpyrotic Cosmology
• Non-Gaussian Density Fluctuations from Entropically Generated Curvature Perturbations in Ekpyrotic Models
• Signatures of Non-Gaussianity in the Curvaton Model
• Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies
• Non-gaussianity from the trispectrum in general single field inflation
• CMB Anisotropies at Second-Order II: Analytical Approach
• 21-cm Background Anisotropies Can Discern Primordial Non-Gaussianity
• Non-gaussianity from the bispectrum in general multiple field inflation
• Simple Bounds from the Perturbative Regime of Inflation
• Inflation from Wrapped Branes
• Reconstructing a general inflationary action
• Non-Gaussian Correlations Outside the Horizon
• The radiative transfer for polarized radiation at second order in cosmological perturbations
• Fine-Tuning in DBI Inflationary Mechanism
• A Tree Theorem for Inflation
• Where does Cosmological Perturbation Theory Break Down?
• Trispectrum versus Bispectrum in Single-Field Inflation

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• On Features and Nongaussianity from Inflationary Particle Production
• A parton picture of de Sitter space during slow-roll inflation
• Stochastic Bias from Non-Gaussian Initial Conditions
• Bispectrum signatures of a modified vacuum in single field inflation with a small speed of sound
• Resonant Trispectrum and a Dozen More Primordial N-point functions
• Attractive Lagrangians for Noncanonical Inflation
• Nongaussianity from Particle Production During Inflation
• Inflation in Motion: Unitarity Constraints in Effective Field Theories with Broken Lorentz Symmetry
• Stochastic eternal inflation is in the swampland
• Bounds on non-adiabatic evolution in single-field inflation
• Feeding your Inflaton: Non-Gaussian Signatures of Interaction Structure
• Initial Conditions for Non-Canonical Inflation
• Relations between canonical and non-canonical inflation
• Large Deviations in the Early Universe
• Preheating in Dirac-Born-Infeld inflation
• Power-counting during single-field slow-roll inflation
• Loop Corrections to Cosmological Perturbations in Multi-field Inflationary Models
• Preheating with the Brakes On: The Effects of a Speed Limit
• Keeping an Eye on DBI: Power-counting for small-$c_s$ Cosmology
• Cosmological correlation functions in scalar and vector inflationary models
• A Tail of Eternal Inflation
• Aspects of inflation and the very early universe