Nonperturbative resummation of de Sitter infrared logarithms in the large-N limit

TL;DR

This paper investigates the nonperturbative behavior of light scalar fields in de Sitter space, revealing how infrared logarithms can be resummed in the large-N limit to modify power laws and demonstrate effective decoupling of scales.

Contribution

It provides a nonperturbative resummation method for infrared logarithms in de Sitter space using the large-N limit, showing the emergence of anomalous dimensions.

Findings

Infrared logarithms can be resummed to modify power-law behavior.

High momentum modes influence infrared modes only through a renormalization factor.

The approach demonstrates effective decoupling of high and low energy physics in expanding space.

Abstract

We study the O(N) scalar field theory with quartic self-coupling in de Sitter space. When the field is light in units of the expansion rate, perturbative methods break down at very low momenta due to large infrared logarithmic terms. Using the nonperturbative large-N limit, we compute the four-point vertex function in the deep infrared regime. The resummation of an infinite series of perturbative (bubble) diagrams leads to a modified power law which is analogous to the generation of an anomalous dimension in critical phenomena. We discuss in detail the role of high momentum (subhorizon) modes, including the issue of renormalization, and show that they influence the dynamics of infrared (superhorizon) modes only through a constant renormalization factor. This provides an explicit example of effective decoupling between high and low energy physics in an expanding space-time.