Complex geodesics in de Sitter space

TL;DR

This paper investigates the role of complex geodesics in de Sitter space to understand two-point functions of scalar fields, resolving a puzzle about spacelike separated points and exploring implications for de Sitter holography.

Contribution

It introduces the use of complex geodesics in de Sitter space to evaluate two-point functions and discusses one-loop corrections, advancing understanding of quantum fields in curved spacetime.

Findings

Complex geodesics connect spacelike separated points in de Sitter space.

One-loop corrections modify the two-point function in the semiclassical approximation.

Implications for de Sitter holography are discussed.

Abstract

The two-point function of a free massive scalar field on a fixed background can be evaluated in the large mass limit by using a semiclassical geodesic approximation. In de Sitter space, however, this poses a puzzle. Certain spacelike separated points are not connected by real geodesics despite the corresponding two-point function in the Bunch-Davies state being non-vanishing. We resolve this puzzle by considering complex geodesics after analytically continuing to the sphere. We compute one-loop corrections to the correlator and discuss the implications of our results to de Sitter holography.