Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions

TL;DR

This paper investigates the limitations of large-order perturbation theory in describing the non-perturbative phenomena of scalar fields in de Sitter and anti de Sitter spaces, highlighting the need for non-perturbative analysis.

Contribution

It demonstrates that perturbative expansions are insufficient to capture non-perturbative effects in curved spacetime quantum field theories, contrasting with known results in flat spacetime.

Findings

Perturbative series are divergent and non-alternating in de Sitter space.

Effective Lagrangian remains real despite particle production.

Full non-perturbative analysis resolves the apparent puzzle.

Abstract

We analyze the large-order behavior of the perturbative weak-field expansion of the effective Lagrangian density of a massive scalar in de Sitter and anti de Sitter space, and show that this perturbative information is not sufficient to describe the non-perturbative behavior of these theories, in contrast to the analogous situation for the Euler-Heisenberg effective Lagrangian density for charged scalars in constant electric and magnetic background fields. For example, in even dimensional de Sitter space there is particle production, but the effective Lagrangian density is nevertheless real, even though its weak-field expansion is a divergent non-alternating series whose formal imaginary part corresponds to the correct particle production rate. This apparent puzzle is resolved by considering the full non-perturbative structure of the relevant Feynman propagators, and cannot be resolved solely from the perturbative expansion.