CFT Perspective On de-Sitter Cosmological Correlators

TL;DR

This paper explores the application of conformal field theory principles to de Sitter cosmological correlators, revealing a non-unitary Euclidean AdS approach that simplifies calculations and uncovers fundamental properties of late-time correlators.

Contribution

It introduces a non-unitary Euclidean AdS framework to compute de Sitter correlators, establishing their CFT structure and spectral properties, including a non-perturbative unitarity criterion.

Findings

Perturbative expansion of late-time correlators derived from non-unitary Euclidean AdS Lagrangian.

Constructed an OPE expansion and limited the operator spectrum of de Sitter correlators.

Computed tree-level and one-loop exchange diagrams confirming spectral density features.

Abstract

We investigate the principles of quantum field theory using a stiff de Sitter space. We demonstrate that a non-unitary Lagrangian on a Euclidean AdS geometry can produce the perturbative expansion of late-time correlation functions to all orders. This discovery greatly simplifies perturbative computations while also allowing us to prove fundamental features of these correlators, which are part of a Euclidean CFT. This allows us to construct an OPE expansion, limit the operator spectrum, and deduce the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function. In general, the standard CFT concept of unitarity does not apply to dimensions and OPE coefficients. Rather, the positivity of the spectral density represents the unitarity of the de Sitter theory. This assertion is non-perturbative and does not depend on the use of Euclidean AdS Lagrangians. In a scalar theory, we compute tree-level and entire one-loop-resummed exchange diagrams to demonstrate and verify these characteristics. In the spectrum density, an exchanged particle shows up as a resonant characteristic that may be helpful in experimental searches.