Holographic non-Gaussianities in general single-field inflation

TL;DR

The paper develops a holographic framework for general single-field inflation by mapping inflationary dynamics to a relevant deformation of a UV CFT and evaluating correlators via conformal perturbation theory. It first computes the UV bispectrum using AdS/Witten diagrams, reproducing standard slow-roll shapes and showing consistency relations from conformal symmetry, then extends to the IR by all-orders resummation of perturbations, yielding red-tilted spectra and complete bispectrum shapes in the slow-roll regime. The results connect holographic CFT data (beta functions, derivative couplings, and conformal dimensions) to inflationary observables, and demonstrate exact agreement with known inflationary formulas in the appropriate limits. This approach offers a unified, model-independent route to capture non-Gaussianities across UV and IR scales, with implications for derivative interactions and cosmological collider phenomenology.

Abstract

We use holographic techniques to compute inflationary non-Gaussianities for general single-field inflation, including models with a non-trivial sound speed. In this holographic approach, the inflationary dynamics is captured by a relevant deformation of the dual conformal field theory (CFT) in the UV, while the inflationary correlators are computed by conformal perturbation theory. In this paper, we discuss the effects of higher derivative operators, such as $(\partial_μφ\partial^μφ)^{m}$, which are known to induce a non-trivial sound speed and source potentially large non-Gaussianities. We compute the full inflationary bispectra from the deformed CFT correlators. We also discuss the squeezed limit of the bispectra from the viewpoint of operator product expansions. As is generic in the holographic description of inflation, our power spectrum is blue tilted in the UV region. We extend our bispectrum computation to the IR region by resumming the conformal perturbations to all orders. We provide a self-consistent setup which reproduces a red tilted power spectrum, as well as all possible bispectrum shapes in the slow-roll regime.

Figures (9)

• Figure 1: A sketch of the bulk and the dual CFT description of the cosmic evolution. From the bulk perspective (right figure), the inflaton starts from the grey ball on the top of the potential and rolls all the way down to the bottom of the potential. From the CFT perspective (left figure) such an evolution is identified with an RG flow connecting two conformal fixed points.
• Figure 2: Illustration of the slow-roll potential $V_{\rm s.r.}(\phi)$.
• Figure 3: The Witten diagram for $\langle O_0 ({\boldsymbol k}_1) O_0 ({\boldsymbol k}_2) O_0 ({\boldsymbol k}_3) O^{2m-3}_0 ({\boldsymbol 0}) \rangle^\prime_{\rm CFT}$. The black line denotes the bulk-boundary propagator $\mathcal{K}_{\boldsymbol k_i}(z)$. The red line represents the zero-momentum bulk-boundary propagator $\mathcal{K}_{\boldsymbol 0}(z)$.
• Figure 4: The effective bulk-boundary propagator is essentially taking all contributions of zero momentum legs (indicated in red). When the bulk point is pulled to the boundary according to \ref{['bbtobb']}, it is exactly the two-point function of the perturbed CFT.
• Figure 5: The diagrammatic representation of the integral \ref{['effective_g_3']}. The black double line denotes the effective bulk-boundary propagator ${\boldsymbol{K}}_{\boldsymbol k_i}(z)$.