One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics

TL;DR

This paper investigates the perturbativity constraints in single-field inflation models with ultra slow-roll phases, analyzing loop corrections to primordial power spectra and their implications for primordial black hole formation.

Contribution

It provides a detailed analysis of loop corrections in USR inflation, demonstrating their significance and limitations for PBH formation scenarios, and clarifies the nature of spectral features like the dip.

Findings

Loop corrections remain within a few percent of the tree-level spectrum.

Perturbativity constraints do not rule out PBH formation via USR.

The dip in the power spectrum is an artifact of tree-level calculations.

Abstract

We discuss the issue of perturbativity in single-field inflationary models with a phase of ultra slow-roll (USR) tailor suited to generate an order-one abundance of primordial black holes (PBHs). More in detail, we impose the condition that loop corrections made up of short-wavelength modes enhanced by the USR dynamics do not alter the tree-level power spectrum of curvature perturbations. In our analysis, the USR phase is preceded and followed by two stages of ordinary slow-roll (SR), and we model the resulting SR/USR/SR dynamics using both instantaneous and smooth transitions. Focusing on scales relevant for CMB observations, we find that it is not possible, with these arguments, to rule out the scenario of PBH formation via USR, not even in the limit of instantaneous transition. However, we also find that loop corrections of short modes on the power spectrum of long modes, even though not large enough to violate perturbativity requirements, remain appreciable and, most importantly, are not tamed in realistic realisations of smooth SR/USR/SR transitions. This makes perturbativity a powerful theoretical tool to constrain USR dynamics. We extend the analysis at any scale beyond those relevant for CMB observations. We find that loop corrections of short modes remain within the few percent if compared to the tree-level power spectrum. However, we also find one notable exception of phenomenological relevance: we show that the so-called dip in the power spectrum of curvature perturbation is an artifact of the tree-level computation.