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Stochastic origin of primordial fluctuations in the Sky

Sayantan Choudhury

TL;DR

Understanding how primordial fluctuations seed primordial black holes (PBHs) requires going beyond Gaussian perturbations. The authors apply a soft-de Sitter EFT (SdSET) generalization of stochastic inflation to a model-independent, single-field setting, using Langevin dynamics and the Fokker-Planck equation together with stochastic-$\delta N$ to model the IR soft modes and UV-to-IR noise. They show that the stochastic-EFT approach can bypass previous no-go theorems and yields PBH masses across a broad range $M_{\rm PBH} \sim O(10^{-8}-10^{11})\,M_{\odot}$, with analytic estimates of non-Gaussian parameters $f_{NL}$, $\tau_{NL}$, and $g_{NL}$ in drift-dominated regimes and PBH abundance from diffusion tails. This framework provides a model-independent, non-perturbative bridge between inflationary microphysics and PBH production, with implications for cosmology and gravitational-wave phenomenology.

Abstract

We provide a study of the effects of the Effective Field Theory (EFT) generalisation of stochastic inflation on the production of primordial black holes (PBHs) in a model-independent single-field context. We demonstrate how the scalar perturbations' Infra-Red (IR) contributions and the emerging Fokker-Planck equation driving the probability distribution characterise the Langevin equations for the ``soft" modes in the quasi-de Sitter background. Both the classical-drift and quantum-diffusion-dominated regimes undergo a specific analysis of the distribution function using the stochastic-$δN$ formalism, which helps us to evade a no-go theorem on the PBH mass. Using the EFT-induced alterations, we evaluate the local non-Gaussian parameters in the drift-dominated limit.

Stochastic origin of primordial fluctuations in the Sky

TL;DR

Understanding how primordial fluctuations seed primordial black holes (PBHs) requires going beyond Gaussian perturbations. The authors apply a soft-de Sitter EFT (SdSET) generalization of stochastic inflation to a model-independent, single-field setting, using Langevin dynamics and the Fokker-Planck equation together with stochastic- to model the IR soft modes and UV-to-IR noise. They show that the stochastic-EFT approach can bypass previous no-go theorems and yields PBH masses across a broad range , with analytic estimates of non-Gaussian parameters , , and in drift-dominated regimes and PBH abundance from diffusion tails. This framework provides a model-independent, non-perturbative bridge between inflationary microphysics and PBH production, with implications for cosmology and gravitational-wave phenomenology.

Abstract

We provide a study of the effects of the Effective Field Theory (EFT) generalisation of stochastic inflation on the production of primordial black holes (PBHs) in a model-independent single-field context. We demonstrate how the scalar perturbations' Infra-Red (IR) contributions and the emerging Fokker-Planck equation driving the probability distribution characterise the Langevin equations for the ``soft" modes in the quasi-de Sitter background. Both the classical-drift and quantum-diffusion-dominated regimes undergo a specific analysis of the distribution function using the stochastic- formalism, which helps us to evade a no-go theorem on the PBH mass. Using the EFT-induced alterations, we evaluate the local non-Gaussian parameters in the drift-dominated limit.

Paper Structure

This paper contains 6 sections, 6 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Stochastic EFT for PBH formation
  3. A short note on stochastic $\delta N$ formalism in EFT
  4. PDFs and PBHs as an outcome of Fokker-Planck equation
  5. What is the big deal with the stochastic EFT framework?
  6. Discussion

Figures (3)

  • Figure 1: This diagram shows that during inflation, modes go from the Sub-Horizon to the Horizon crossing, where they face stochastic effects before re-entering the Horizon.
  • Figure 2: A schematic changing behaviour of coarse-grained curvature perturbation with e-folds $N$.
  • Figure 3: Behaviour of the \ref{['f3a']} PDF with stochastic variable ${\cal N}$ and \ref{['f3b']} scalar power spectrum amplitude needed to attain a sufficient PBH mass fraction $\beta$ with wave number.