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

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.

31+16 pages, 16 figures. v3. Corrected typos in equations

References in corpus (165)

• Planck 2018 results. X. Constraints on inflation
• The Standard Model Higgs boson as the inflaton
• The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set
• Constraints on Primordial Black Holes
• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• A new approach to the evolution of cosmological perturbations on large scales
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• A general proof of the conservation of the curvature perturbation
• Primordial Black Holes as Dark Matter: Recent Developments
• Density Perturbations and Black Hole Formation in Hybrid Inflation
• Primordial Black Holes as a dark matter candidate
• Cosmological perturbations
• Semiclassicality and Decoherence of Cosmological Perturbations
• Primordial black holes from single field models of inflation
• Super-Horizon Scale Dynamics of Multi-Scalar Inflation
• Threshold of primordial black hole formation
• On initial conditions for the Hot Big Bang
• Preheating in the Standard Model with the Higgs-Inflaton coupled to gravity
• Primordial black hole dark matter from single field inflation
• Dynamics of Primordial Black Hole Formation
• Inflation and squeezed quantum states
• Black hole formation in the Friedmann universe: Formulation and computation in numerical relativity
• Steepest growth of the power spectrum and primordial black holes
• Computations of primordial black hole formation
• Black Hole Relics and Inflation: Limits on Blue Perturbation Spectra
• Primordial Black Holes and Slow-Roll Violation
• Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations
• Primordial black hole formation in the early universe: critical behaviour and self-similarity
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Primordial Black Hole production in Critical Higgs Inflation
• Quantum-to-classical transition for fluctuations in the early Universe
• Single Field Double Inflation and Primordial Black Holes
• Stochastic Quantum Gravitational Inflation
• The abundance of primordial black holes depends on the shape of the inflationary power spectrum
• A universal threshold for primordial black hole formation
• Calculating the mass spectrum of primordial black holes
• Correlation Functions in Stochastic Inflation
• The Threshold for Primordial Black Hole Formation: a Simple Analytic Prescription
• Relieving the Hubble tension with primordial magnetic fields
• Constraints on the density perturbation spectrum from primordial black holes
• Enhancement of superhorizon scale inflationary curvature perturbations
• Quantum Fluctuations, Decoherence of the Mean Field, and Structure Formation in the Early Universe
• Higgs inflation
• Black Hole Remnants and Dark Matter
• A new calculation of the mass fraction of primordial black holes
• Cosmological long-wavelength solutions and primordial black hole formation
• Primordial black holes and second order gravitational waves from ultra-slow-roll inflation
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Quantum-to-classical Transition of Cosmological Perturbations for Non-vacuum Initial States
• Quantum diffusion during inflation and primordial black holes
• The exponential tail of inflationary fluctuations: consequences for primordial black holes
• The Ineludible non-Gaussianity of the Primordial Black Hole Abundance
• Primordial Black Holes from Inflation and Quantum Diffusion
• Primordial black hole formation and abundance: contribution from the non-linear relation between the density and curvature perturbation
• Non-linear metric perturbations and production of primordial black holes
• Primordial Black Holes from Polynomial Potentials in Single Field Inflation
• Pointer states for primordial fluctuations in inflationary cosmology
• Primordial Black Holes and Local Non-Gaussianity in Canonical Inflation
• On the quantum origin of the seeds of cosmic structure
• Curvature profiles as initial conditions for primordial black hole formation
• PBH abundance from random Gaussian curvature perturbations and a local density threshold
• Violent Preheating in Inflation with Nonminimal Coupling
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
• Cosmological Inflation and the Quantum Measurement Problem
• Shortcomings in the Understanding of Why Cosmological Perturbations Look Classical
• Single-field inflation, anomalous enhancement of superhorizon fluctuations, and non-Gaussianity in primordial black hole formation
• Inflationary perturbations near horizon crossing
• The primordial black hole formation criterion re-examined: parameterisation, timing, and the choice of window function
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• On the Decoherence of Primordial Fluctuations During Inflation
• Infrared Correlations in de Sitter Space: Field Theoretic vs. Stochastic Approach
• Preheating in Palatini Higgs inflation
• Non-linear statistics of primordial black holes from gaussian curvature perturbations
• Quantum diffusion beyond slow-roll: implications for primordial black-hole production
• The Formation Probability of Primordial Black Holes
• Inflationary Perturbations: the Cosmological Schwinger Effect
• Infrared dynamics in de Sitter space from Schwinger-Dyson equations
• Classical approximation to quantum cosmological correlations
• Ultra-slow-roll inflation with quantum diffusion
• Dissecting the growth of the power spectrum for primordial black holes
• Curvature perturbation at the local extremum of the inflaton's potential
• An effective field theory during inflation: reduced density matrix and its quantum master equation
• On the robustness of the primordial power spectrum in renormalized Higgs inflation
• Analytical thresholds for black hole formation in general cosmological backgrounds
• Planck scale black hole dark matter from Higgs inflation
• Identifying the most crucial parameters of the initial curvature profile for primordial black hole formation
• Stochastic Inflation:The Quantum Phase Space Approach
• Preheating after Higgs Inflation: Self-Resonance and Gauge boson production
• Stochastic inflation in phase space: Is slow roll a stochastic attractor?
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• On "dynamical mass" generation in Euclidean de Sitter space
• Primordial black holes in peak theory with a non-Gaussian tail
• Stochastic inflation beyond slow roll
• A new algorithm for calculating the curvature perturbations in stochastic inflation
• Effective noise in stochastic description of inflation
• A Leading Logarithm Approximation for Inflationary Quantum Field Theory
• Gravitational Uncertainty and Black Hole Remnants
• Effect of nonlinearity between density and curvature perturbations on the primordial black hole formation
• On the Decoherence of Primordial Fluctuations During Inflation
• Preheating after multifield inflation with nonminimal couplings, III: Dynamical spacetime results
• The Decay of the Standard Model Higgs after Inflation
• Simulation of primordial black hole formation using pseudo-spectral methods
• Combined Preheating on the lattice with applications to Higgs inflation
• On the slope of curvature power spectrum in non-attractor inflation
• Stochastic Ultra Slow Roll Inflation
• An analytic approach to non-slow-roll inflation
• Non-Gaussian Formation of Primordial Black Holes: Effects on the Threshold
• An effective field theory during inflation II: stochastic dynamics and power spectrum suppression
• Formation of MACHO-Primordial Black Holes in Inflationary Cosmology
• Inflation Induced Planck-Size Black Hole Remnants As Dark Matter
• Effective long wavelength scalar dynamics in de Sitter
• Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
• Emergence of classicality for primordial fluctuations: Concepts and analogies
• Can Primordial Black Holes be a Significant Part of Dark Matter ?
• Proposal for gravitational direct detection of dark matter
• Black Hole Relics in String Gravity: Last Stages of Hawking Evaporation
• Overshooting, Critical Higgs Inflation and Second Order Gravitational Wave Signatures
• Primordial black holes and oscillating gravitational waves in slow-roll and slow-climb inflation with an intermediate non-inflationary phase
• Power spectrum in stochastic inflation
• Failure of the stochastic approach to inflation beyond slow-roll
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Threshold of Primordial Black Hole Formation in Nonspherical Collapse
• Stochastic Inflation and the Lower Multipoles in the CMB Anisotropies
• Application of peaks theory to the abundance of primordial black holes
• Scalar correlation functions in de Sitter space from the stochastic spectral expansion
• Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
• Canonical transformations and squeezing formalism in cosmology
• Energy distribution and equation of state of the early Universe: matching the end of inflation and the onset of radiation domination
• Influence of Super-Horizon Scales on Cosmological Observables Generated during Inflation
• Statistical nature of infrared dynamics on de Sitter background
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Stochastic Effects in Hybrid Inflation
• Backreaction and Stochastic Effects in Single Field Inflation
• Inflation is always semi-classical: Diffusion domination overproduces Primordial Black Holes
• A non-Gaussian landscape
• Stochastic inflation at all order in slow-roll parameters: foundations
• Small-scale clumping at recombination and the Hubble tension
• What happens when the inflaton stops during inflation
• Peculiar Relics from Primordial Black Holes in the Inflationary Paradigm
• Can all the infrared secular growth really be understood as increase of classical statistical variance?
• Lagrangian Formulation of Stochastic Inflation: A Recursive Approach
• Stochastic approach to inflation II: classicality, coarse-graining and noises
• Functional renormalization group in stochastic inflation
• Production of Primordial Black Holes via Single Field Inflation and Observational Constraints
• Critical review of prevailing explanations for the emergence of classicality in cosmology
• Preheating the Universe from the Standard Model Higgs
• The quantum Fokker-Planck equation of stochastic inflation
• On the Reliability of the Langevin Pertubative Solution in Stochastic Inflation
• Stochastic Dynamics of Coarse-Grained Quantum Fields in Inflationary Universe
• Emergence of classical behavior in the early universe
• Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere
• Inflationary stochastic anomalies
• On Preheating in Higgs Inflation
• Window function dependence of the novel mass function of primordial black holes
• Recursive Stochastic Effects in Valley Hybrid Inflation
• Stochastic non-attractor inflation
• The Quantum State of Inflationary Perturbations
• Numerically modeling stochastic inflation in slow-roll and beyond
• Tachyonic Preheating in Plateau Inflation
• Stellar Signatures of Inhomogeneous Big Bang Nucleosynthesis
• Peak statistics for the primordial black hole abundance
• Full nonlinear growing and decaying modes of superhorizon curvature perturbations
• Quantum decoherence of primordial perturbations through nonlinear scaler-tensor interaction

Cited by in corpus (57)

• Cosmology with the Laser Interferometer Space Antenna
• Inflation and Primordial Black Holes
• Anatomy of single-field inflationary models for primordial black holes
• Logarithmic Duality of the Curvature Perturbation
• Primordial Black Holes
• Statistics of coarse-grained cosmological fields in stochastic inflation
• One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics
• Primordial black hole dark matter from inflation: the reverse engineering approach
• Stochastic constant-roll inflation and primordial black holes
• Primordial black holes and gravitational waves induced by exponential-tailed perturbations
• Review on stochastic approach to inflation
• The separate-universe approach and sudden transitions during inflation
• Primordial black holes ensued from exponential potential and coupling parameter in nonminimal derivative inflation model
• Ultra-Slow-Roll Inflation on the Lattice I: Backreaction and Nonlinear Effects
• Numerical simulations of stochastic inflation using importance sampling
• Hamiltonian formalism for cosmological perturbations: the separate-universe approach
• Large fluctuations and Primordial Black Holes
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Numerical stochastic inflation constrained by frozen noise
• Enhanced power on small scales and evolution of quantum state of perturbations in single and two field inflationary models
• Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation
• Primordial black holes and inflation from double-well potentials
• Stochastic Inflation in General Relativity
• STOLAS: STOchastic LAttice Simulation of cosmic inflation
• Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes
• Constraints on ultra-slow-roll inflation from the third LIGO-Virgo observing run
• Stochastic inflation beyond slow roll: noise modelling and importance sampling
• Quantum loop corrections in the modified gravity model of Starobinsky inflation with primordial black hole production
• Quantum diffusion and large primordial perturbations from inflation
• Gravitational waves in ultra-slow-roll and their anisotropy at two loops
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Computing First-Passage Times with the Functional Renormalisation Group
• Ultra-Slow-Roll Inflation on the Lattice II: Nonperturbative Curvature Perturbation
• Stochastic inflation with gradient interactions
• Probing Reheating Phase via Non-Helical Magnetogenesis and Secondary Gravitational Waves
• Stochastic inflation and non-perturbative power spectrum beyond slow roll
• Spatial correlations of dark energy from quantum fluctuations in inflation
• Non-Gaussianities and Primordial Black Holes
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Quantitative classicality in cosmological interactions during inflation
• Stochastic origin of primordial fluctuations in the Sky
• An analytical approximation of the evolution of the primordial curvature perturbation in the ultraslow-roll inflation
• Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation
• Primordial black holes from the ultraslow-roll phase in the inflaton--curvaton mixed field inflation
• Inflationary relics from an Ultra-Slow-Roll plateau
• Minimal Magnetogenesis: The Role of Inflationary Perturbations and ALPs, and Its Gravitational Wave Signatures
• Constraints on ultra-slow-roll inflation with the NANOGrav 15-Year Dataset
• Stochastic Inflation in Numerical Relativity
• Improved model of large-field inflation with primordial black hole production in Starobinsky-like supergravity
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Inflationary $\alpha$-Attractor Models with Singular Derivative of Potential
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• Eternal inflation near inflection points: a challenge to primordial black hole models
• Deviations from Gaussian White Noise in Stochastic Inflation
• Constant-roll inflation and primordial black holes within Barrow entropic framework
• 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