Analyticity and Unitarity for Cosmological Correlators

TL;DR

This paper explores the fundamental properties of quantum field theory in de Sitter space, revealing a non-unitary Euclidean AdS representation that simplifies calculations and clarifies the spectral density's positivity as a sign of unitarity.

Contribution

It establishes a novel equivalence between late-time correlators in de Sitter space and a Euclidean AdS Lagrangian, enabling new insights into the spectral density and operator spectrum.

Findings

Spectral density positivity indicates de Sitter unitarity.

Explicit calculations confirm theoretical predictions.

Resonant features in spectral density relate to exchanged particles.

Abstract

We study the fundamentals of quantum field theory on a rigid de Sitter space. We show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. This finding simplifies dramatically perturbative computations, as well as allows us to establish basic properties of these correlators, which comprise a Euclidean CFT. We use this to infer the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function, to derive an OPE expansion, and to constrain the operator spectrum. Generically, dimensions and OPE coefficients do not obey the usual CFT notion of unitarity. Instead, unitarity of the de Sitter theory manifests itself as the positivity of the spectral density. This statement does not rely on the use of Euclidean AdS Lagrangians and holds non-perturbatively. We illustrate and check these properties by explicit calculations in a scalar theory by computing first tree-level, and then full one-loop-resummed exchange diagrams. An exchanged particle appears as a resonant feature in the spectral density which can be potentially useful in experimental searches.