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

Abstract

Using an imaginary time formalism, we propose a consistent renormalizable perturbation theory of a scalar field in a non-trivial α vacuum in de Sitter space. Although one representation of the effective action involves non-local interactions between anti-podal points, we argue the theory leads to causal physics when continued to real-time, 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.