Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Local non-Gaussianity from inflation

David Wands

TL;DR

This work reviews how local non-Gaussianity arises from inflationary physics using the δN formalism, which expresses the primordial curvature perturbation as a local expansion in initial Gaussian field perturbations. It covers diagrammatic methods to compute tree-level and loop corrections to the power spectrum and higher-point functions, and presents explicit expressions for f_NL, g_NL, and related parameters in both single-field and multi-field contexts. The paper then surveys concrete models—curvaton, modulated decay, multi-field inflation, and ekpyrotic scenarios—highlighting how each yields distinctive non-Gaussian signatures and potential isocurvature modes, along with current observational bounds. Finally, it discusses the prospects for current and future observations (CMB and LSS) to detect or constrain local-type non-Gaussianity and stresses the need for tailored theoretical templates to distinguish between competing scenarios.

Abstract

The non-Gaussian distribution of primordial perturbations has the potential to reveal the physical processes at work in the very early Universe. Local models provide a well-defined class of non-Gaussian distributions that arise naturally from the non-linear evolution of density perturbations on super-Hubble scales starting from Gaussian field fluctuations during inflation. I describe the delta-N formalism used to calculate the primordial density perturbation on large scales and then review several models for the origin of local primordial non-Gaussianity, including the cuvaton, modulated reheating and ekpyrotic scenarios. I include an appendix with a table of sign conventions used in specific papers.

Local non-Gaussianity from inflation

TL;DR

This work reviews how local non-Gaussianity arises from inflationary physics using the δN formalism, which expresses the primordial curvature perturbation as a local expansion in initial Gaussian field perturbations. It covers diagrammatic methods to compute tree-level and loop corrections to the power spectrum and higher-point functions, and presents explicit expressions for f_NL, g_NL, and related parameters in both single-field and multi-field contexts. The paper then surveys concrete models—curvaton, modulated decay, multi-field inflation, and ekpyrotic scenarios—highlighting how each yields distinctive non-Gaussian signatures and potential isocurvature modes, along with current observational bounds. Finally, it discusses the prospects for current and future observations (CMB and LSS) to detect or constrain local-type non-Gaussianity and stresses the need for tailored theoretical templates to distinguish between competing scenarios.

Abstract

The non-Gaussian distribution of primordial perturbations has the potential to reveal the physical processes at work in the very early Universe. Local models provide a well-defined class of non-Gaussian distributions that arise naturally from the non-linear evolution of density perturbations on super-Hubble scales starting from Gaussian field fluctuations during inflation. I describe the delta-N formalism used to calculate the primordial density perturbation on large scales and then review several models for the origin of local primordial non-Gaussianity, including the cuvaton, modulated reheating and ekpyrotic scenarios. I include an appendix with a table of sign conventions used in specific papers.

Paper Structure

This paper contains 13 sections, 55 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. The $\delta N$ expansion
  3. Diagrammatic approach
  4. Single-field vs multi-variate local models
  5. Isocurvature non-Gaussianity
  6. Models of non-Gaussianity
  7. Single inflaton
  8. Curvaton
  9. Multiple-field inflation
  10. Modulated decay
  11. Ekpyrotic model
  12. Conclusions
  13. Sign conventions

Figures (1)

  • Figure 1: Power spectrum diagrams for $\delta N$ expansion with Gaussian fields (a) at tree level, and (b) one loop, corresponding to each term in Eq. (\ref{['P1loop']}).