Non-Gaussian Inflationary Perturbations from the dS/CFT Correspondence

TL;DR

This work uses the dS/CFT correspondence to compute the holographic three-point function of the operator dual to inflaton perturbations in single-field, slow-roll inflation, providing a nontrivial consistency check against Maldacena’s bulk QFT results. By constructing bulk-to-boundary and bulk-to-bulk propagators, performing holographic renormalization, and carefully accounting for boundary terms from derivative interactions, the authors derive the holographic one-, two-, and three-point functions and show that the inflaton three-point function reproduced from the boundary CFT matches the standard Maldacena result. The analysis also demonstrates how boundary contributions can be absorbed via a field redefinition and outlines how the method could generalize to higher-point functions within (n−1)th-order perturbation theory. Overall, the paper reinforces the viability of dS/CFT as a tool for inflationary phenomenology and offers insights into quantum gravity in de Sitter spacetime.

Abstract

We use the dS/CFT correspondence and bulk gravity to predict the form of the renormalized holographic three-point correlation function of the operator which is dual to the inflaton field perturbation during single-field, slow-roll inflation. Using Maldcaena's formulation of the correspondence, this correlator can be related to the three-point function of the curvature perturbation generated during single-field inflation, and we find exact agreement with previous bulk QFT calculations. This provides a consistency check on existing derivations of the non-Gaussianity from single-field inflation and also yields insight into the nature of the dS/CFT correspondence. As a result of our calculation, we obtain the properly renormalized dS/CFT one-point function, including boundary contributions where derivative interactions are present in the bulk. In principle, our method may be employed to derive the n-point correlators of the inflationary curvature perturbation within the context of (n-1)th-order perturbation theory, rather than nth-order theory as in conventional approaches.