A radial variable for de Sitter two-point functions

TL;DR

This paper introduces a new radial invariant for de Sitter two-point functions, enabling a convergent series expansion and analytic continuation, which enhances understanding of quantum fields in curved spacetime.

Contribution

The paper proposes a novel radial variable for de Sitter two-point functions, providing a convergent series expansion and non-perturbative generalization for scalar operators.

Findings

Series expansion of two-point functions converges exponentially with positive coefficients.

Analytic continuation from sphere to de Sitter domain is established.

Paths between de Sitter, sphere, and Euclidean AdS are contained within the complex domain.

Abstract

We introduce a "radial" two-point invariant for quantum field theory in de Sitter (dS) analogous to the radial coordinate used in conformal field theory. We show that the two-point function of a free massive scalar in the Bunch-Davies vacuum has an exponentially convergent series expansion in this variable with positive coefficients only. Assuming a convergent K\"all\'en-Lehmann decomposition, this result is then generalized to the two-point function of any scalar operator non-perturbatively. A corollary of this result is that, starting from two-point functions on the sphere, an analytic continuation to an extended complex domain is admissible. dS two-point configurations live inside or on the boundary of this domain, and all the paths traced by Wick rotations between dS and the sphere or between dS and Euclidean Anti-de Sitter are also contained within this domain.