Primordial black holes from inflation: on the decoupling between large and small scales

TL;DR

This paper discusses how large-scale cosmic microwave background modes remain unaffected by small-scale perturbations that could produce primordial black holes, ensuring consistency of inflation models with observations.

Contribution

It demonstrates that 1-loop back-reaction effects do not couple large and small scales under certain assumptions, supporting the viability of PBH formation models.

Findings

1-loop back-reaction is due to non-linear super-horizon evolution or corrected initial conditions.

Large scales decouple from short-scale enhancements under scale separation and adiabaticity.

PBH production does not disrupt large-scale CMB predictions in single-field inflation.

Abstract

Primordial black holes (PBHs) can be produced from inflation if the primordial curvature power spectrum is strongly enhanced on scales much shorter than those probed by cosmic microwave background (CMB) experiments. In single-field models this typically requires a transient departure from slow-roll, attractor dynamics, for example realized through a brief ultra-slow-roll phase. In these scenarios, there is reasonable concern that large-scale modes, whose statistics is tightly constrained by CMB observations, might back-react to the amplified perturbations on much shorter scales. In a perturbative expansion for the long-mode power spectrum, this effect first appears at 1-loop. In these proceedings we summarize recent works on this issue, based on the application of the separate-universe framework and its general extension with multi-point propagators. We show that back-reaction at 1-loop is due to either (i) non-linear super-horizon evolution, or (ii) 1-loop-corrected initial conditions. By assuming separation of scales and adiabaticity of the long mode, we show that the 1-loop back-reaction is not observable and large scales decouple from enhanced short ones. While we demonstrate that PBH production within single-field inflation does not disrupt large-scale predictions, we close by discussing scenarios to which our results do not apply.