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Primordial black hole formation and abundance: contribution from the non-linear relation between the density and curvature perturbation
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abstract
The formation and abundance of primordial black holes (PBHs) arising from the curvature perturbation $\zeta$ is studied. The non-linear relation between $\zeta$ and the density contrast $\delta$ means that, even when $\zeta$ has an exactly Gaussian distribution, significant non-Gaussianities affecting PBH formation must be considered. Numerical simulations are used to investigate the critical value and the mass of PBHs which form, and peaks theory is used to calculate the mass fraction of the universe collapsing to form PBHs at the time of formation. A formalism to calculate the total present day PBH abundance and mass function is also derived. It is found that the abundance of PBHs is very sensitive to the non-linear effects, and that the power spectrum $\mathcal{P}_\zeta$ must be a factor of $\sim2$ larger to produce the same number of PBHs as the linear model (where the exact value depends on the critical value for a region to collapse and form a PBH). This also means that the derived constraints on the small-scale power spectrum from constraints on the abundance of PBHs are weaker by the same factor.
Forward citations
Cited by 8 Pith papers
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The statistics of curvature-profile dispersion in primordial black hole formation
Shape dispersion around the average peak profile is a genuine statistical ingredient: rare deformed curvature profiles can dominate primordial black hole formation when the power spectrum is broad or non-Gaussianity i...
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Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls
Tensor perturbations from FOPT and domain-wall sources are claimed to induce second-order scalar perturbations large enough to form primordial black holes, potentially all of the dark matter.
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Revisiting PBH accretion, evaporation and their cosmological consequences
Relativistic accretion onto Kerr primordial black holes gives roughly 4.5x mass growth and fast spin-down, strengthening BBN bounds, lowering the survival mass to ~2.7e14 g, and erasing the high-frequency stochastic g...
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Purely quadratic non-Gaussianity from tachyonic instability: Primordial black holes and scalar-induced gravitational waves
Purely quadratic non-Gaussianity from tachyonic instability allows narrow curvature spectra to exponentially suppress primordial black hole overproduction via correlation coefficient ρ approaching -1 while retaining s...
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Primordial black hole dark matter from ultra-slow-roll inflation in Horndeski gravity
A kinetic cubic Horndeski coupling creates an ultra-slow-roll phase that amplifies curvature perturbations enough to produce asteroid-mass primordial black holes, potentially 90% of dark matter.
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Are Primordial Black Holes Truly Fine-Tuned?
Using a normalized sensitivity measure γ=c/c̄, the authors find γ≈1 for three single-field ultra-slow-roll inflation models and conclude PBH production is not technically unnatural.
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Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer
A Bayesian analysis shows that a future sub-solar PBH detection would make the primordial SIGW interpretation of PTA data favored over the SMBH interpretation, but this preference is driven by the detection prior.
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Gravitational Waves from Primordial Black Holes: Connecting Low-Frequency Scalar-Induced Signatures to High-Frequency Binary Mergers
For monochromatic primordial black holes, the low-frequency scalar-induced gravitational-wave peak and the high-frequency binary-merger ISCO frequency are linked by fISCO ≈ 3.4×10^20 Hz × (fSIGW/Hz)^2.
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