Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Four-point Correlator in Multifield Inflation, the Operator Product Expansion and the Symmetries of de Sitter

A. Kehagias, A. Riotto

TL;DR

This work investigates multifield inflation where light spectator fields source the curvature perturbation, employing the operator product expansion and de Sitter conformal symmetry to analyze the non-Gaussian four-point function in the squeezed limit. It demonstrates that the non-universal, horizon-crossing NG can dominate over universal superhorizon contributions and often has a distinct shape not reducible to products of power spectra. Two independent derivations (an OPE-based approach and Cardy’s conformal inversion trick) plus a consistency check establish the form and magnitude of the non-universal trispectrum, emphasizing the role of operator mixing and couplings. The findings underscore the need to incorporate non-universal NG contributions when interpreting large-scale structure observables, such as halo clustering and bias, and motivate further work to quantify these effects in data.

Abstract

We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. We exploit the operator product expansion and partly the symmetries present during the de Sitter epoch to characterize the non-Gaussian four-point correlator in the squeezed limit. We point out that the contribution to it from the intrinsic non-Gaussianity of the light fields at horizon crossing can be larger than the usually studied contribution arising on superhorizon scales and it comes with a different shape. Our findings indicate that particular attention needs to be taken when studying the effects of the primordial NG on real observables, such as the clustering of dark matter halos.

The Four-point Correlator in Multifield Inflation, the Operator Product Expansion and the Symmetries of de Sitter

TL;DR

This work investigates multifield inflation where light spectator fields source the curvature perturbation, employing the operator product expansion and de Sitter conformal symmetry to analyze the non-Gaussian four-point function in the squeezed limit. It demonstrates that the non-universal, horizon-crossing NG can dominate over universal superhorizon contributions and often has a distinct shape not reducible to products of power spectra. Two independent derivations (an OPE-based approach and Cardy’s conformal inversion trick) plus a consistency check establish the form and magnitude of the non-universal trispectrum, emphasizing the role of operator mixing and couplings. The findings underscore the need to incorporate non-universal NG contributions when interpreting large-scale structure observables, such as halo clustering and bias, and motivate further work to quantify these effects in data.

Abstract

We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. We exploit the operator product expansion and partly the symmetries present during the de Sitter epoch to characterize the non-Gaussian four-point correlator in the squeezed limit. We point out that the contribution to it from the intrinsic non-Gaussianity of the light fields at horizon crossing can be larger than the usually studied contribution arising on superhorizon scales and it comes with a different shape. Our findings indicate that particular attention needs to be taken when studying the effects of the primordial NG on real observables, such as the clustering of dark matter halos.

Paper Structure

This paper contains 13 sections, 85 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Some general considerations about non-Gaussianities
  3. Non-Gaussianities and the conformal symmetries of de Sitter
  4. Non-Gaussianities and the Operator product expansion
  5. The three-point correlator in the squeezed limit
  6. The four-point correlator in the collapsed limit
  7. The four-point correlator in the squeezed limit
  8. A consistency check
  9. The four-point correlator in the squeezed limit: alternative methods
  10. First method
  11. Second method: Cardy's trick
  12. On the non-universal contributions to NG
  13. Conclusions

Figures (1)

  • Figure 1: Tree diagrams contributing to the modulation of the three-point function of short wavelength modes (continues lines) in the background of a long wavelength mode (dashed lines).