Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production

Abstract

We consider quantum diffusion in ultra-slow-roll (USR) inflation. Using the $\Delta N$ formalism, we present the first stochastic calculation of the probability distribution $P(\mathcal{R})$ of the curvature perturbation during USR. We capture the non-linearity of the system, solving the coupled evolution of the coarse-grained background with random kicks from the short wavelength modes, simultaneously with the mode evolution around the stochastic background. This leads to a non-Markovian process from which we determine the highly non-Gaussian tail of $P(\mathcal{R})$. Studying the production of primordial black holes in a viable model, we find that stochastic effects during USR increase their abundance by a factor $\sim 10^5$ compared to the Gaussian approximation.

5+3 pages, 2 figures. v3: Corrected typos in equations

References in corpus (26)

• The Standard Model Higgs boson as the inflaton
• Primordial Black Holes as Dark Matter: Recent Developments
• Primordial Black Holes as a dark matter candidate
• Primordial black hole dark matter from single field inflation
• Primordial Black Holes and Slow-Roll Violation
• Calculating the mass spectrum of primordial black holes
• The Threshold for Primordial Black Hole Formation: a Simple Analytic Prescription
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• The exponential tail of inflationary fluctuations: consequences for primordial black holes
• Ultra slow-roll inflation demystified
• Non-linear statistics of primordial black holes from gaussian curvature perturbations
• Ultra-slow-roll inflation with quantum diffusion
• Classical approximation to quantum cosmological correlations
• Analytical thresholds for black hole formation in general cosmological backgrounds
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• 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
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
• Canonical transformations and squeezing formalism in cosmology
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Critical point Higgs inflation in the Palatini formulation
• The quantum Fokker-Planck equation of stochastic inflation
• Window function dependence of the novel mass function of primordial black holes
• Numerically modeling stochastic inflation in slow-roll and beyond
• Peak statistics for the primordial black hole abundance

Cited by in corpus (84)

• Cosmology with the Laser Interferometer Space Antenna
• Inflation and Primordial Black Holes
• Anatomy of single-field inflationary models for primordial black holes
• Non-perturbative non-Gaussianity and primordial black holes
• Logarithmic Duality of the Curvature Perturbation
• Primordial black holes in peak theory with a non-Gaussian tail
• Primordial Black Holes
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Highly non-Gaussian tails and primordial black holes from single-field inflation
• Amplification of Primordial Perturbations from the Rise or Fall of the Inflaton
• Peaks and primordial black holes: the effect of non-Gaussianity
• Squeezed bispectrum and one-loop corrections in transient constant-roll inflation
• One Small Step for an Inflaton, One Giant Leap for Inflation: a novel non-Gaussian tail and primordial black holes
• Primordial black holes from single-field inflation: a fine-tuning audit
• Primordial Black Holes Arise When The Inflaton Falls
• Primordial black holes from stochastic tunnelling
• Primordial black hole formation during the QCD phase transition: threshold, mass distribution and abundance
• Statistics of coarse-grained cosmological fields in stochastic inflation
• One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics
• Induced gravitational waves from the cosmic coincidence
• Stochastic constant-roll inflation and primordial black holes
• Primordial black holes and gravitational waves induced by exponential-tailed perturbations
• Non-Gaussianity and Secondary Gravitational Waves from Primordial Black Holes Production in $\alpha$-attractor Inflation
• Large power spectrum and primordial black holes in the effective theory of inflation
• Inflation is always semi-classical: Diffusion domination overproduces Primordial Black Holes
• Stochastic inflation at all order in slow-roll parameters: foundations
• Planck Constraints and Gravitational Wave Forecasts for Primordial Black Hole Dark Matter Seeded by Multifield 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
• A Note on the Abundance of Primordial Black Holes: Use and Misuse of the Metric Curvature Perturbation
• Rare Events Are Nonperturbative: Primordial Black Holes From Heavy-Tailed Distributions
• Highly asymmetric probability distribution from a finite-width upward step during inflation
• Missing one-loop contributions in secondary gravitational waves
• Clustering of primordial black holes from quantum diffusion during inflation
• Numerical simulations of stochastic inflation using importance sampling
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Primordial black holes and induced gravitational waves from logarithmic non-Gaussianity
• Mechanism of primordial black holes production and secondary gravitational waves in $\alpha$-attractor Galileon inflationary scenario
• Numerical stochastic inflation constrained by frozen noise
• Uphill inflation
• Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation
• Primordial black holes and inflation from double-well potentials
• Unveiling the nonlinear dynamics of a rolling axion during inflation
• Primordial black holes from an inflationary potential valley
• STOLAS: STOchastic LAttice Simulation of cosmic inflation
• Constraints on ultra-slow-roll inflation from the third LIGO-Virgo observing run
• Sudden braking and turning with a two-field potential bump: primordial black hole formation
• Stochastic inflation beyond slow roll: noise modelling and importance sampling
• Smooth coarse-graining and colored noise dynamics in stochastic inflation
• Quantum diffusion and large primordial perturbations from inflation
• Primordial black holes: constraints, potential evidence and prospects
• Gravitational waves in ultra-slow-roll and their anisotropy at two loops
• The cosmic coincidences of primordial-black-hole dark matter
• Constraining the history of reheating with the NANOGrav 15-year data
• Computing First-Passage Times with the Functional Renormalisation Group
• Baryogenesis from ultra-slow-roll inflation
• Ultra-Slow-Roll Inflation on the Lattice II: Nonperturbative Curvature Perturbation
• A numerical approach to stochastic inflation and primordial black holes
• Stochastic inflation with gradient interactions
• Stochastic inflation and non-perturbative power spectrum beyond slow roll
• Stochastic origin of primordial fluctuations in the Sky
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Non-Gaussianities and Primordial Black Holes
• Non-gaussianities for primordial black hole formation
• An analytical approximation of the evolution of the primordial curvature perturbation in the ultraslow-roll inflation
• Primordial black holes from the ultraslow-roll phase in the inflaton--curvaton mixed field inflation
• Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation
• Dip and non-linearity in the curvature perturbation from inflation with a transient non-slow-roll stage
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Primordial black holes from a curvaton: the role of bimodal distributions
• Constraints on ultra-slow-roll inflation with the NANOGrav 15-Year Dataset
• Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Stochastic Inflation in Numerical Relativity
• 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
• The hand-made tail: Non-perturbative tails from multifield inflation
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting
• Primordial black holes from the perturbations in the inflaton potential in peak theory
• Primordial black hole formation in k-inflation models
• Excursion-set for Primordial Black Holes I: white noise and moving barrier