Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation

TL;DR

This paper investigates how stochastic noise influences primordial black hole formation during ultra-slow-roll inflation, revealing that stochastic effects can significantly alter PBH abundance predictions and emphasizing the importance of non-Markovian dynamics.

Contribution

It introduces a detailed numerical analysis of stochastic effects on PBH production in USR inflation, accounting for non-linearity and non-Markovian effects, and compares different potential models.

Findings

Stochastic effects can enhance PBH abundance by up to 8 orders of magnitude.

Non-Markovian effects are subleading in the dynamics.

The usual approximation of stochastic kicks can significantly misestimate PBH abundance.

Abstract

We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations. We consider the non-linearity of the system by consistently taking into account the noise dependence on the inflaton perturbations, while evolving the perturbations on the coarse-grained background affected by the noise. We capture in this way the non-Markovian nature of the dynamics, and demonstrate that non-Markovian effects are subleading. Using the $\Delta N$ formalism, we find the probability distribution $P(\mathcal{R})$ of the comoving curvature perturbation $\mathcal{R}$. We consider inflationary potentials that fit the CMB and lead to PBH dark matter with $i)$ asteroid, $ii)$ solar, or $iii)$ Planck mass, as well as $iv)$ PBHs that form the seeds of supermassive black holes. We find that stochastic effects enhance the PBH abundance by a factor of $\mathcal{O}(10)-\mathcal{O}(10^8)$, depending on the PBH mass. We also show that the usual approximation, where stochastic kicks depend only on the Hubble rate, either underestimates or overestimates the abundance by orders of magnitude, depending on the potential. We evaluate the gauge dependence of the results, discuss the quantum-to-classical transition, and highlight open issues of the application of the stochastic formalism to USR inflation.