Real-Time Perturbation Theory in de Sitter Space

TL;DR

This paper investigates scalar quantum field theory in de Sitter space, highlighting issues with perturbative definitions, the role of the Bunch-Davies vacuum, and implications for coupling to gravity.

Contribution

It analyzes different perturbative approaches in de Sitter space and clarifies the conditions under which the theory remains well-defined, emphasizing the significance of the Bunch-Davies vacuum.

Findings

Feynman diagram approach leads to pinch singularities and ill-defined perturbation theory.

Imaginary time continuation yields well-defined correlation functions.

Coupling to gravity introduces unavoidable acausal effects.

Abstract

We consider scalar field theory in de Sitter space with a general vacuum invariant under the continuously connected symmetries of the de Sitter group. We begin by reviewing approaches to define this as a perturbative quantum field theory. One approach leads to Feynman diagrams with pinch singularities in the general case, which renders the theory perturbatively ill-defined. Another approach leads to well-defined perturbative correlation functions on the imaginary time continuation of de Sitter space. When continued to real-time, a path integral with a non-local action generates the time-ordered correlators. Curiously, observables built out of local products of the fields show no sign of this non-locality. However once one couples to gravity, we show acausal effects are unavoidable and presumably make the theory ill-defined. The Bunch-Davies vacuum state is the unique de Sitter invariant state that avoids these problems.