Real-time perturbation theory in de Sitter space

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 nonlocality. 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.