Numerical stochastic inflation constrained by frozen noise

Abstract

Stochastic inflation can resolve strong inflationary perturbations, which seed primordial black holes. I present a fast and accurate way to compute these perturbations in typical black hole producing single-field models, treating the short-wavelength Fourier modes beyond the de Sitter approximation. The squeezing and freezing of the modes reduces the problem to one dimension, and the resulting new form of the stochastic equations, dubbed `constrained stochastic inflation,' can be solved efficiently with semi-analytical techniques and numerical importance sampling. In an example case, the perturbation distribution is resolved in seconds deep into its non-Gaussian tail, a speed-up of factor $10^9$ compared to a previous study. Along the way, I comment on the role of the momentum constraint in stochastic inflation.

34 pages, 8 figures, 1 table. v2: Minor revisions in text. Published version

References in corpus (16)

• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Primordial Black Holes as Dark Matter: Recent Developments
• The merger rate of primordial-black-hole binaries
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Inflationary Perturbations: the Cosmological Schwinger Effect
• Classical approximation to quantum cosmological correlations
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
• Stochastic Inflation at NNLO
• Power spectrum in stochastic inflation
• Primordial black holes from stochastic tunnelling
• Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• The quantum Fokker-Planck equation of stochastic inflation
• Perturbations in stochastic inflation
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase

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• Large fluctuations and Primordial Black Holes
• Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation
• Stochastic Inflation in General Relativity
• STOLAS: STOchastic LAttice Simulation of cosmic inflation
• Stochastic inflation beyond slow roll: noise modelling and importance sampling
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Computing First-Passage Times with the Functional Renormalisation Group
• Stochastic inflation and non-perturbative power spectrum beyond slow roll
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Quantitative classicality in cosmological interactions during inflation
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Stochastic Inflation in Numerical Relativity
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Bunch-Davies initial conditions and non-perturbative inflationary dynamics in Numerical Relativity
• Eternal inflation near inflection points: a challenge to primordial black hole models
• Time-reversed Stochastic Inflation
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function