Peak statistics for the primordial black hole abundance

Abstract

The primordial black hole (PBH) abundance evaluated by the conventional Press-Schechter (PS) probability distribution is shown to be equivalent to the high-peak limit of a special point-like peak statistics via unphysical dimensionality reduction of the Bardeen-Bond-Kaiser-Szalay (BBKS) theory. The fact that PBHs are formed at high peak values ${\nu }_c\gg 1$ leads to a systematic bias proportional to ${\nu }_c^3$ between the predictions of the PS method and the physical BBKS peak theory in a general three-dimensional spatial configuration. As long as realistic PBHs are collapsed from three-dimensional density peaks in space, the systematic bias led by ${\nu }_c^3$ implies a significant underestimation of the PBH abundance reported by the PS method. For the inflationary spectrum in the narrow-spike class, the underestimation in the extended mass functions is further enlarged by at least a factor of $10^{2.5}$ in all mass range, indicating a severer constraint to models in the favor of considering PBHs as all dark matter in a certain mass range.

arXiv comment28 +1 pages, 11 figures; references added; version matched with publication; extended clarification on the inaccuracy of the Press-Schechter approach

References in corpus (44)

• New cosmological constraints on primordial black holes
• Primordial Black Holes as Dark Matter
• Primordial Black Holes
• Microlensing constraints on primordial black holes with the Subaru/HSC Andromeda observation
• Primordial black holes from single field models of inflation
• Primordial black hole constraints for extended mass functions
• Gravitational Waves Induced by non-Gaussian Scalar Perturbations
• Threshold of primordial black hole formation
• Near-Critical Gravitational Collapse and the Initial Mass Function of Primordial Black Holes
• Dynamics of Primordial Black Hole Formation
• Computations of primordial black hole formation
• Primordial black hole formation in the early universe: critical behaviour and self-similarity
• Primordial black holes as a dark matter candidate are severely constrained by the Galactic Center 511 keV gamma-ray line
• Gravitational Wave signatures of inflationary models from Primordial Black Hole Dark Matter
• Primordial black hole formation in the radiative era: investigation of the critical nature of the collapse
• Femtolensing by Dark Matter Revisited
• The abundance of primordial black holes depends on the shape of the inflationary power spectrum
• The Primordial Black Hole Dark Matter - LISA Serendipity
• Inflationary Primordial Black Holes as All Dark Matter
• A universal threshold for primordial black hole formation
• Primordial Black Holes as All Dark Matter
• Calculating the mass spectrum of primordial black holes
• Gravitational waves at interferometer scales and primordial black holes in axion inflation
• Revisiting constraints on asteroid-mass primordial black holes as dark matter candidates
• Voyager 1 $e^{\pm }$ Further Constrain Primordial Black Holes as Dark Matter
• Primordial black holes with an accurate QCD equation of state
• Clusters of primordial black holes
• Primordial Black Holes from Inflation and non-Gaussianity
• Microlensing and dynamical constraints on primordial black hole dark matter with an extended mass function
• Primordial black holes as a tool for constraining non-Gaussianity
• Non-Gaussian Fluctuations and Primordial Black Holes from Inflation
• Gravitational-Wave Constraints on the Abundance of Primordial Black Holes
• Double inflation as a single origin of primordial black holes for all dark matter and LIGO observations
• Primordial Black Holes from String Inflation
• Single-field inflation, anomalous enhancement of superhorizon fluctuations, and non-Gaussianity in primordial black hole formation
• Constraints on Primordial Black Holes with Extended Mass Functions
• Primordial black holes as biased tracers
• Constraining primordial black hole masses with the isotropic gamma ray background
• Identifying the most crucial parameters of the initial curvature profile for primordial black hole formation
• Effect of nonlinearity between density and curvature perturbations on the primordial black hole formation
• Simulation of primordial black hole formation using pseudo-spectral methods
• Influence of large local and non-local bispectra on primordial black hole abundance
• Microlensing of X-ray Pulsars: a Method to Detect Primordial Black Hole Dark Matter
• Gravitational waves from a curvaton model with blue spectrum

Cited by in corpus (13)

• Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• The Gravitational-Wave Physics II: Progress
• PBH formation from spherically symmetric hydrodynamical perturbations: a review
• Primordial Black Holes
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• On Primordial Black Holes and secondary gravitational waves generated from inflation with solo/multi-bumpy potential
• The Interplay between the Dark Matter Axion and Primordial Black Holes
• The cosmic coincidences of primordial-black-hole dark matter
• Baryogenesis from ultra-slow-roll inflation
• Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer
• Primordial blackhole formation: Exploring chaotic potential with a sharp step via the GLMS perspective
• Simulation of Primordial Black Holes with large negative non-Gaussianity