A note on alpha-vacua and interacting field theory in de Sitter space

TL;DR

This paper develops a consistent, renormalizable perturbation theory for scalar fields in alpha-vacua of de Sitter space, demonstrating causality, stability, and constructing the stress-energy tensor.

Contribution

It introduces a renormalizable perturbation framework for scalar fields in alpha-vacua, addressing non-local interactions and proving stability and causality.

Findings

The theory is causal despite non-local interactions.

The stress-energy tensor remains real, indicating stability.

A spectral theorem for the interacting two-point function is established.

Abstract

We set up a consistent renormalizable perturbation theory of a scalar field in a nontrivial alpha vacuum in de Sitter space. Although one representation of the effective action involves non-local interactions between anti-podal points, we show the theory leads to causal physics, and we prove a spectral theorem for the interacting two-point function. We construct the renormalized stress energy tensor and show this develops no imaginary part at leading order in the interactions, consistent with stability.