Inflationary Fossils Beyond Perturbation Theory

TL;DR

This paper connects two methods for analyzing long perturbation modes in inflation, demonstrating their agreement at first order and proposing the non-perturbative approach as an all-orders extension.

Contribution

It clarifies the applicability of a non-perturbative technique and shows it matches perturbative results, extending the Fossils' approach to all orders.

Findings

Non-perturbative approach matches perturbative results at first order.

The non-perturbative technique likely resums all orders of perturbation theory.

Six cases, including violation of consistency conditions, confirm the approach's validity.

Abstract

In this work we provide the missing link between two approaches aimed at characterizing the effect of long perturbation modes in Inflation. We consider the Inflationary Fossils' approach (arXiv:1203.0302 and related works) that characterizes the power-spectrum of the inflaton field in presence of other long and non dynamical fossil fields, and a technique, appeared in arXiv:2103.09244, that computes, beyond perturbation theory, the power-spectrum of a scalar field in presence of a large fluctuation of a second field. We clarify a few points on the applicability of the non-perturbative technique. We prove in six distinct cases, one involving a violation of the consistency conditions, that the non-perturbative approach, once expanded to first order in the coupling, matches the perturbative result following the Fossils' approach. We believe that this non-perturbative technique extends to all orders the Fossils' approach, resumming infinitely many diagrams of standard in-in perturbation theory.