De Sitter Diagrammar and the Resummation of Time

TL;DR

This paper introduces a diagrammatic method to resum infrared divergences in inflationary spacetimes, connecting quantum fluctuations to a stochastic classical description, and offering a systematic approach to address the infrared pathology in de Sitter space.

Contribution

It presents a novel diagrammatic analysis and resummation technique for infrared divergences in inflationary quantum field theory, linking it to stochastic inflation and de Sitter holography.

Findings

Diagrammatic determination of leading-log contributions.

Superhorizon sector described by semiclassical stochastic equations.

Systematic and improvable approximation of quantum field theory.

Abstract

Light scalars in inflationary spacetimes suffer from logarithmic infrared divergences at every order in perturbation theory. This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy "landscape" on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation, the infrared divergences appear to spoil computability. Some form of renormalization group approach is thus motivated to resum the log divergences of conformal time. Such a resummation may provide insight into De Sitter holography. We present here a novel diagrammatic analysis of these infrared divergences and their resummation. Basic graph theory observations and momentum power counting for the in-in propagators allow a simple and insightful determination of the leading-log contributions. One thus sees diagrammatically how the superhorizon sector consists of a semiclassical theory with quantum noise evolved by a first-order, interacting classical equation of motion. This rigorously leads to the "Stochastic Inflation" ansatz developed by Starobinsky to cure the scalar infrared pathology nonperturbatively. Our approach is a controlled approximation of the underlying quantum field theory and is systematically improvable.