Quantum diffusion beyond slow-roll: implications for primordial black-hole production

TL;DR

This paper investigates how quantum diffusion effects beyond slow-roll inflation influence primordial black-hole production, revealing significant enhancements in the power spectrum and non-Gaussianities that boost PBH abundance.

Contribution

It develops a new methodology to analyze quantum diffusion beyond slow-roll in inflationary models, applying it to a toy potential with a quasi-inflection point.

Findings

Quantum noise enhances the power spectrum beyond slow-roll.

Non-Gaussian corrections, especially kurtosis, become significant.

PBH production is substantially boosted due to quantum diffusion effects.

Abstract

Primordial black-holes (PBH) can be produced in single-field models of inflation with a quasi-inflection point in the potential. In these models, a large production of PBHs requires a deviation from the slow-roll (SR) trajectory. In turn, this SR violation can produce an exponential growth of quantum fluctuations. We study the back-reaction of these quantum modes on the inflationary dynamics using stochastic inflation in the Hamilton-Jacobi formalism. We develop a methodology to solve quantum diffusion beyond SR in terms of the statistical moments of the probability distribution. We apply these techniques to a toy model potential with a quasi-inflection point. We find that there is an enhancement of the power spectrum due to the dominance of the stochastic noise in the phase beyond SR. Moreover, non-Gaussian corrections become as well relevant with a large positive kurtosis. Altogether, this produces a significant boost of PBH production. We discuss how our results extend to other single-field models with similar dynamics. We conclude that the abundance of PBHs in this class of models should be revisited including quantum diffusion.