Interacting Quantum Field Theory in de Sitter Vacua

TL;DR

This paper analyzes interacting quantum field theory in de Sitter space, arguing that the Mottola-Allen vacua are artifacts of free-field theory and that correlation-function analyticity uniquely selects the Euclidean (Bunch-Davies) vacuum for a consistent perturbation theory. It shows that MA-vacua introduce nonanalytic, acausal, and non-thermal features that render loop amplitudes ill-defined and that the KMS condition is violated, unlike the Euclidean vacuum which supports a Källén-Lehmann structure and standard axioms. The main contribution is to establish analyticity as a fundamental criterion for viability of QFT in curved spacetime and to demonstrate that only the Euclidean vacuum yields a well-defined interacting theory, with implications for inflationary cosmology and holography in time-dependent backgrounds. The results constrain trans-Planckian vacuum choices and argue for a principled vacuum selection based on analyticity, with potential links to dS/CFT and holographic formulations.

Abstract

We discuss interacting quantum field theory in de Sitter space and argue that the Mottola-Allen vacuum ambiguity is an artifact of free field theory. The nature of the nonthermality of the MA-vacua is also clarified. We propose analyticity of correlation functions as a fundamental requirement of quantum field theory in curved spacetimes. In de Sitter space, this principle determines the vacuum unambiguously and facilitates the systematic development of perturbation theory.

Figures (5)

• Figure 1: Causal relations to the antipodal point.
• Figure 2: Simple tree diagram.
• Figure 3: Penrose diagram for three points.
• Figure 4: Self-energy diagram.
• Figure 5: Pinched singularities.