Propagators in de Sitter space

TL;DR

This paper develops a method to calculate de Sitter invariant propagators for scalar fields by defining vacuum states as instantaneous ground states, addressing ambiguities in curved spacetime quantum field theory.

Contribution

It introduces a novel approach for computing vacuum wave functions and propagators in de Sitter space, ensuring invariance and consistency with path integral methods.

Findings

De Sitter invariant propagators are obtained in various coordinate patches.

The in-out propagator has a finite massless limit in de Sitter space.

The proposed propagators satisfy Polyakov's composition law.

Abstract

In a spacetime with no global timelike Killing vector, we do not have a natural choice for the vacuum state of matter fields, leading to an ambiguity in defining the Feynman propagators. In this paper, taking the vacuum state to be the instantaneous ground state of the Hamiltonian at each moment, we develop a method for calculating wave functions associated with the vacuum and the corresponding in-in and in-out propagators. We apply this method to free scalar field theory in de Sitter space and obtain de Sitter invariant propagators in various coordinate patches. We show that the in-out propagator in the Poincare patch has a finite massless limit in a de Sitter invariant form. We argue and numerically check that our in-out propagators agree with those obtained by a path integral with the standard i\epsilon prescription, and identify the condition on a foliation of spacetime under which such coincidence can happen for the foliation. We also show that the in-out propagators satisfy Polyakov's composition law. Several applications of our framework are also discussed.