Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter

TL;DR

This paper applies conformal field theory techniques, specifically the operator product expansion, to analyze inflationary correlators during de Sitter space, revealing new insights into their shapes and fundamental inequalities.

Contribution

It introduces the use of OPE in inflationary correlators, derives the shape of four-point functions in collapsed limits, and confirms the Suyama-Yamaguchi inequality under broader conditions.

Findings

OPE characterizes inflationary correlators in specific limits.

The shape of four-point correlators in the collapsed limit is determined.

The Suyama-Yamaguchi inequality holds even with non-Gaussian light fields.

Abstract

We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. The corresponding perturbations are both scale invariant and special conformally invariant. We exploit the operator product expansion technique of conformal field theories to study the inflationary correlators enjoying the symmetries present during the de Sitter epoch. The operator product expansion is particularly powerful in characterizing inflationary correlation functions in two observationally interesting limits, the squeezed limit of the three-point correlator and the collapsed limit of the four-point correlator. Despite the fact that the shape of the four-point correlators is not fixed by the symmetries of de Sitter, its exact shape can be found in the collapsed limit making use of the operator product expansion. By employing the fact that conformal invariance imposes the two-point cross-correlations of the light fields to vanish unless the fields have the same conformal weights, we are able to show that the Suyama-Yamaguchi inequality relating the coefficients $f_{\rm NL}$ of the bispectrum in the squeezed limit and $\tau_{\rm NL}$ of the trispectrum in the collapsed limit also holds when the light fields are intrinsically non-Gaussian. In fact, we show that the inequality is valid irrespectively of the conformal symmetry, being just a consequence of fundamental physical principles, such as the short-distance expansion of operator products. The observation of a strong violation of the inequality will then have profound implications for inflationary models as it will imply either that multifield inflation cannot be responsible for generating the observed fluctuations independently of the details of the model or that some new non-trivial degrees of freedom play a role during inflation.