Large Order Behavior of Quasiclassical Euclidean Gravity in Minisuperspace Models

TL;DR

This paper shows that in certain minisuperspace models, the perturbation series of quasiclassical Euclidean gravity is asymptotic with factorial growth at large orders, implying it behaves like an effective field theory.

Contribution

It demonstrates the factorial large-order behavior of the perturbation expansion in two minisuperspace models, suggesting an asymptotic series structure in Euclidean quantum gravity.

Findings

Perturbation series exhibits factorial growth at large orders.

Expansion is asymptotic, indicating effective field theory behavior.

Series may be Borel summable depending on classical solutions.

Abstract

We demonstrate in two minisuperspace models that a perturbation expansion of quasiclassical Euclidean gravity has a factorial dependence on the order of the term at large orders. This behavior indicates that the expansion is an asymptotic series which is suggestive of an effective field theory. The series may or may not be Borel summable depending on the classical solution expanded around. We assume that only the positive action classical solution contributes to path integrals. We close with some speculative discussion on possible implications of the asymptotic nature of the expansion.