de Sitter Vacua, Renormalization and Locality

TL;DR

This paper investigates the renormalization of quantum fields in de Sitter space, identifying two invariant vacua that support consistent perturbation theory, and discusses implications for the evolution of such systems.

Contribution

It characterizes the conditions under which quantum field theories in de Sitter space have well-defined perturbation expansions, focusing on the Euclidean and analytically continued vacua.

Findings

Only two invariant vacua support consistent perturbation series.

The Euclidean vacuum and a related analytically continued vacuum are identified as viable.

Perturbation series in the second vacuum exhibit divergences at the origin, affecting predictability.

Abstract

We analyze the renormalization properties of quantum field theories in de Sitter space and show that only two of the maximally invariant vacuum states of free fields lead to consistent perturbation expansions. One is the Euclidean vacuum, and the other can be viewed as an analytic continuation of Euclidean functional integrals on $RP^d$. The corresponding Lorentzian manifold is the future half of global de Sitter space with boundary conditions on fields at the origin of time. We argue that the perturbation series in this case has divergences at the origin, which render the future evolution of the system indeterminate without a better understanding of high energy physics.