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Primordial Non-Gaussianities from Inflation Models

Xingang Chen

TL;DR

This pedagogical review analyzes how inflationary dynamics imprint primordial non-Gaussianities in the bispectrum. It develops the in-in formalism for time-dependent backgrounds, explains why the simplest single-field slow-roll models yield tiny non-Gaussianities, and surveys mechanisms that can produce observable signals, including non-canonical kinetic terms, sharp and resonant features, non-Bunch-Davies vacua, and quasi-single-field dynamics. The work provides explicit shape templates (equilateral, folded, local-like, resonant) and discusses how their running and correlations can be used to distinguish between models, with concrete examples such as DBI inflation. Overall, it links theoretical inflationary mechanisms to measurable non-Gaussian signatures in the CMB and large-scale structure, offering a practical framework for data-driven model discrimination.

Abstract

This is a pedagogical review on primordial non-Gaussianities from inflation models. We introduce formalisms and techniques that are used to compute such quantities. We review different mechanisms which can generate observable large non-Gaussianities during inflation, and distinctive signatures they leave on the non-Gaussian profiles. They are potentially powerful probes to the dynamics of inflation. We also provide a non-technical and qualitative summary of the main results and underlying physics.

Primordial Non-Gaussianities from Inflation Models

TL;DR

This pedagogical review analyzes how inflationary dynamics imprint primordial non-Gaussianities in the bispectrum. It develops the in-in formalism for time-dependent backgrounds, explains why the simplest single-field slow-roll models yield tiny non-Gaussianities, and surveys mechanisms that can produce observable signals, including non-canonical kinetic terms, sharp and resonant features, non-Bunch-Davies vacua, and quasi-single-field dynamics. The work provides explicit shape templates (equilateral, folded, local-like, resonant) and discusses how their running and correlations can be used to distinguish between models, with concrete examples such as DBI inflation. Overall, it links theoretical inflationary mechanisms to measurable non-Gaussian signatures in the CMB and large-scale structure, offering a practical framework for data-driven model discrimination.

Abstract

This is a pedagogical review on primordial non-Gaussianities from inflation models. We introduce formalisms and techniques that are used to compute such quantities. We review different mechanisms which can generate observable large non-Gaussianities during inflation, and distinctive signatures they leave on the non-Gaussian profiles. They are potentially powerful probes to the dynamics of inflation. We also provide a non-technical and qualitative summary of the main results and underlying physics.

Paper Structure

This paper contains 20 sections, 154 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Road map
  3. Inflation and density perturbations
  4. In-in formalism and correlation functions
  5. In-in formalism
  6. Mode functions and vacuum
  7. Contractions
  8. Three forms
  9. Summary
  10. A no-go theorem
  11. Beyond the no-go
  12. Inflation model building
  13. Shape and running of bispectra
  14. Single field inflation
  15. Equilateral shape: higher derivative kinetic terms
  16. ...and 5 more sections

Figures (13)

  • Figure 1: An example of Feynman diagram.
  • Figure 2: Momentum configurations: (a) equilateral, (b) squeezed, (c) folded.
  • Figure 3: Shape of $S_\lambda$ in (\ref{['S_lam']}).
  • Figure 4: Shape of $S_c$ in (\ref{['S_c']}).
  • Figure 5: An ansatz (\ref{['ansatz_eq']}) for the equilateral shape.
  • ...and 8 more figures