Clustering of primordial black holes from quantum diffusion during inflation

Abstract

We study how large fluctuations are spatially correlated in the presence of quantum diffusion during inflation. This is done by computing real-space correlation functions in the stochastic-$\delta N$ formalism. We first derive an exact description of physical distances as measured by a local observer at the end of inflation, improving on previous works. Our approach is based on recursive algorithmic methods that consistently include volume-weighting effects. We then propose a "large-volume'' approximation under which calculations can be done using first-passage time analysis only, and from which a new formula for the power spectrum in stochastic inflation is derived. We then study the full two-point statistics of the curvature perturbation. Due to the presence of exponential tails, we find that the joint distribution of large fluctuations is of the form $P({\zeta }_{R_1},{\zeta }_{R_2})=F(R_1,R_2,r)P({\zeta }_{R_1})P({\zeta }_{R_2})$, where ${\zeta }_{R_1}$ and ${\zeta }_{R_2}$ denote the curvature perturbation coarse-grained at radii $R_1$ and $R_2$, around two spatial points distant by $r$. This implies that, on the tail, the reduced correlation function, defined as $P({\zeta }_{R_1}>{\zeta }_{\mathrm{c}},{\zeta }_{R_2}>{\zeta }_{\mathrm{c}})/[P({\zeta }_{R_1}>{\zeta }_{\mathrm{c}})P({\zeta }_{R_2}>{\zeta }_{\mathrm{c}})]-1$, is independent of the threshold value ${\zeta }_{\mathrm{c}}$. This contrasts with Gaussian statistics where the same quantity strongly decays with ${\zeta }_{\mathrm{c}}$, and shows the existence of a universal clustering profile for all structures forming in the exponential tails. Structures forming in the intermediate (i.e. not yet exponential) tails may feature different, model-dependent behaviours.

52 pages, 14 figures. Discussion around Eq.(3.6) expanded, a few minor changes and typos fixed. Some references added. Matches published version in JCAP

References in corpus (67)

• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• A new approach to the evolution of cosmological perturbations on large scales
• A general proof of the conservation of the curvature perturbation
• The inflationary prediction for primordial non-gaussianity
• Super-Horizon Scale Dynamics of Multi-Scalar Inflation
• Black hole formation in the Friedmann universe: Formulation and computation in numerical relativity
• Gravitational Waves from Primordial Black Hole Mergers
• Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations
• Correlation Functions in Stochastic Inflation
• Clusters of primordial black holes
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Observational Evidence for Primordial Black Holes: A Positivist Perspective
• Primordial Black Holes from Inflation and non-Gaussianity
• Cosmological long-wavelength solutions and primordial black hole formation
• Holographic probabilities in eternal inflation
• Quantum diffusion during inflation and primordial black holes
• The exponential tail of inflationary fluctuations: consequences for primordial black holes
• Conserved cosmological perturbations
• Boltzmann brains and the scale-factor cutoff measure of the multiverse
• Primordial non-gaussianity up to all orders: theoretical aspects and implications for primordial black hole models
• Stochastic growth of quantum fluctuations during slow-roll inflation
• On the divergences of inflationary superhorizon perturbations
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• The Clustering Evolution of Primordial Black Holes
• The Spatial Clustering of Primordial Black Holes
• Stationarity of Inflation and Predictions of Quantum Cosmology
• Non-perturbative non-Gaussianity and primordial black holes
• Ultra-slow-roll inflation with quantum diffusion
• Logarithmic Duality of the Curvature Perturbation
• On the merger rate of primordial black holes: effects of nearest neighbours distribution and clustering
• Making predictions in the multiverse
• Correlation function of high-threshold regions and application to the initial small-scale clustering of primordial black holes
• Stochastic inflation in phase space: Is slow roll a stochastic attractor?
• Clustering of primordial black holes: Basic results
• A new algorithm for calculating the curvature perturbations in stochastic inflation
• Primordial Black Holes
• Updating the MACHO fraction of the Milky Way dark halo with improved mass models
• Highly non-Gaussian tails and primordial black holes from single-field inflation
• Multiple Fields in Stochastic Inflation
• Primordial Black Holes from Broad Spectra: Abundance and Clustering
• Power spectrum in stochastic inflation
• Critical Number of Fields in Stochastic Inflation
• Primordial black holes from stochastic tunnelling
• Initial clustering and the primordial black hole merger rate
• Statistics of coarse-grained cosmological fields in stochastic inflation
• Strong constraints on clustered primordial black holes as dark matter
• Clustering of primordial black holes with non-Gaussian initial fluctuations
• Stationary Measure in the Multiverse
• The separate-universe approach and sudden transitions during inflation
• Ruling out Initially Clustered Primordial Black Holes as Dark Matter
• Measure Problem for Eternal and Non-Eternal Inflation
• LIGO/Virgo black holes and dark matter: The effect of spatial clustering
• Squeezed Bispectrum in the $\delta N$ Formalism: Local Observer Effect in Field Space
• Watchers of the multiverse
• Early formation of galaxies initiated by clusters of primordial black holes
• Effect of clustering on primordial black hole microlensing constraints
• Tunneling in Stochastic Inflation
• Highly asymmetric probability distribution from a finite-width upward step during inflation
• A volume-weighted measure for eternal inflation
• Langevin Analysis of Eternal Inflation
• Primordial black holes and their gravitational-wave signatures
• Hamiltonian formalism for cosmological perturbations: the separate-universe approach
• Microlensing constraints on clustered primordial black holes
• Uphill inflation
• Constraining the Initial Primordial Black Hole Clustering with CMB-distortion
• Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation
• Small-scale clustering of Primordial Black Holes: cloud-in-cloud and exclusion effects

Cited by in corpus (22)

• The Science of the Einstein Telescope
• The Open Effective Field Theory of Inflation
• Ultra-Slow-Roll Inflation on the Lattice I: Backreaction and Nonlinear Effects
• Large fluctuations and Primordial Black Holes
• STOLAS: STOchastic LAttice Simulation of cosmic inflation
• Stochastic inflation beyond slow roll: noise modelling and importance sampling
• Quantum diffusion and large primordial perturbations from inflation
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Stochastic inflation with gradient interactions
• Stochastic inflation and non-perturbative power spectrum beyond slow roll
• Stochastic origin of primordial fluctuations in the Sky
• Primordial black holes from a curvaton: the role of bimodal distributions
• 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
• Primordial black holes with mass ratio-modulated initial clustering: merger suppression and projected constraints
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Time-reversed Stochastic Inflation
• Eternal inflation near inflection points: a challenge to primordial black hole models
• Smoluchowski Coagulation Equation and the Evolution of Primordial Black Hole Clusters
• Excursion-set for Primordial Black Holes I: white noise and moving barrier
• Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators
• 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