On the divergences of inflationary superhorizon perturbations

TL;DR

This paper addresses infrared divergences in inflationary cosmological perturbation theory, showing they are regulated by eternal inflation and can be absorbed into redefined background fields, leading to finite, gauge-invariant observables.

Contribution

It demonstrates that infrared divergences can be managed within the stochastic framework using the $ riangle N$ formalism, allowing for finite, renormalization group invariant predictions.

Findings

Infrared divergences are regulated by eternal inflation.

Infrared modes can be absorbed into additive constants.

A non-perturbative, finite relation between two-point correlators is derived.

Abstract

We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that within the stochastic framework they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the $\Delta N$ formalism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for the infrared cutoff would of course be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization group invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.