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Effective Theory of Squeezed Correlation Functions

Mehrdad Mirbabayi, Marko Simonović

TL;DR

The paper develops an effective theory for squeezed-limit correlation functions in quasi-de Sitter inflation by organizing fluctuations into weakly coupled, super-horizon degrees of freedom. It shows that long-wavelength modes act as local backgrounds, enabling a derivative-expansion that yields factorized, power-law squeezed-limit behavior and unifies single-, quasi-single-, and multi-field scenarios; light entropic modes produce calculable consistency relations, while heavy fields $m/H>3/2$ imprint oscillatory, quantum-origin signatures in the squeezed limit. The framework yields model-independent statements about the scaling exponents $\Delta$ and provides unitarity bounds (e.g., on $f_{NL}$ and $\tau_{NL}$) in the multi-field case, as well as practical guidance for observing these signatures in large-scale structure surveys. It also clarifies when OPE intuition is subleading and how heavy-field versus classical long-mode effects distinguish themselves in observable correlators. Overall, the work offers a universal lens to test quasi-de Sitter dynamics and the field content during inflation with current and future cosmological data.

Abstract

Various inflationary scenarios can often be distinguished from one another by looking at the squeezed limit behavior of correlation functions. Therefore, it is useful to have a framework designed to study this limit in a more systematic and efficient way. We propose using an expansion in terms of weakly coupled super-horizon degrees of freedom, which is argued to generically exist in a near de Sitter space-time. The modes have a simple factorized form which leads to factorization of the squeezed-limit correlation functions with power-law behavior in $k_{\rm long}/k_{\rm short}$. This approach reproduces the known results in single-, quasi-single-, and multi-field inflationary models. However, it is applicable even if, unlike the above examples, the additional degrees of freedom are not weakly coupled at sub-horizon scales. Stronger results are derived in two-field (or sufficiently symmetric multi-field) inflationary models. We discuss the observability of the non-Gaussian 3-point function in the large-scale structure surveys, and argue that the squeezed limit behavior has a higher detectability chance than equilateral behavior when it scales as $(k_{\rm long}/k_{\rm short})^Δ$ with $Δ<1$ -- where local non-Gaussianity corresponds to $Δ=0$.

Effective Theory of Squeezed Correlation Functions

TL;DR

The paper develops an effective theory for squeezed-limit correlation functions in quasi-de Sitter inflation by organizing fluctuations into weakly coupled, super-horizon degrees of freedom. It shows that long-wavelength modes act as local backgrounds, enabling a derivative-expansion that yields factorized, power-law squeezed-limit behavior and unifies single-, quasi-single-, and multi-field scenarios; light entropic modes produce calculable consistency relations, while heavy fields imprint oscillatory, quantum-origin signatures in the squeezed limit. The framework yields model-independent statements about the scaling exponents and provides unitarity bounds (e.g., on and ) in the multi-field case, as well as practical guidance for observing these signatures in large-scale structure surveys. It also clarifies when OPE intuition is subleading and how heavy-field versus classical long-mode effects distinguish themselves in observable correlators. Overall, the work offers a universal lens to test quasi-de Sitter dynamics and the field content during inflation with current and future cosmological data.

Abstract

Various inflationary scenarios can often be distinguished from one another by looking at the squeezed limit behavior of correlation functions. Therefore, it is useful to have a framework designed to study this limit in a more systematic and efficient way. We propose using an expansion in terms of weakly coupled super-horizon degrees of freedom, which is argued to generically exist in a near de Sitter space-time. The modes have a simple factorized form which leads to factorization of the squeezed-limit correlation functions with power-law behavior in . This approach reproduces the known results in single-, quasi-single-, and multi-field inflationary models. However, it is applicable even if, unlike the above examples, the additional degrees of freedom are not weakly coupled at sub-horizon scales. Stronger results are derived in two-field (or sufficiently symmetric multi-field) inflationary models. We discuss the observability of the non-Gaussian 3-point function in the large-scale structure surveys, and argue that the squeezed limit behavior has a higher detectability chance than equilateral behavior when it scales as with -- where local non-Gaussianity corresponds to .

Paper Structure

This paper contains 18 sections, 81 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Super-horizon degrees of freedom
  3. Squeezed limit in a classical background field
  4. Massive fields with $1-n_s\ll m^2/H^2 < 9/4$
  5. Squeezed limit and operator product expansion
  6. Entropic perturbations $m/H \ll 1$
  7. Consistency conditions on two-field scenarios
  8. Unitarity constraints on multi-field models
  9. Heavy fields $m/H>3/2$
  10. Quantum versus classical correlation
  11. Prospects in large-scale structure surveys
  12. Conclusions
  13. Purturbative examples of factorization
  14. Fundamental fields
  15. Light fields
  16. ...and 3 more sections

Figures (1)

  • Figure 1: (a) The diagram that corresponds to the squeezed limit bispectrum calculated using OPE (see equation \ref{['OPE']}). Both power spectra are on the short modes. (b) Diagrams for the leading part of the squeezed limit bispectrum given by \ref{['phiphisigma']}. One of the power spectra is on the long mode.