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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 17 Pith papers
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The statistics of curvature-profile dispersion in primordial black hole formation
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Using numerical relativity thresholds, cosmological perturbation theory, and peak theory, the authors derive updated upper limits on the small-scale primordial curvature power spectrum from primordial black hole abund...
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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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Robust {\mu}-distortion constraints on primordial supermassive black holes from cubic (gNL) non-Gaussian perturbations
In the infinite cubic (gNL) non-Gaussianity limit, CMB mu-distortion constraints on the primordial power spectrum amplitude remain close to Gaussian, deviating only at high wavenumbers.
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Light Scalar Fields Foster Production of Primordial Black Holes
A spectator scalar field with minimal coupling can replace ultra-slow-roll with a turn and tachyonic growth mechanism, producing primordial black holes while reducing fine-tuning.
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The Irrelevance of Primordial Black Hole Clustering in the LVK mass range
Initial spatial clustering of primordial black holes is irrelevant for binary mergers in the LVK mass range because FIRAS spectral-distortion constraints limit the clustering scale to below the merger-relevant separat...
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Probing Primordial Black Hole Mergers in Clusters with Pulsar Timing Data
Bayesian analysis of IPTA DR2 shows scalar-induced gravitational waves dominate and PBH merger backgrounds are strongly disfavored relative to an astrophysical SMBHB explanation.
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Testing inflation on all scales: a case study with $\alpha$-attractors
A subset of hybrid alpha-attractor inflation models passes all large- and small-scale constraints and predicts scalar-induced gravitational waves detectable by LISA.
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PBH in single field inflation: the effect of shape dispersion and non-Gaussianities
In a barrier single-field inflation model, primordial black holes form preferentially from false-vacuum bubbles once f_NL exceeds about 3.5, and shape dispersion has little effect on the compaction threshold.
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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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Non-Standard Thermal History and Formation of Primordial Black Holes in Einstein-Gauss-Bonnet Gravity
A tuned Einstein-Gauss-Bonnet inflation model can create primordial black holes from asteroid-sized to tens of solar masses and secondary gravitational waves, with abundances that change dramatically in a stiff post-i...
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Is the formation of primordial black holes from single-field inflation compatible with standard cosmology?
Producing primordial black holes in single-field inflation typically forces more than about 55 e-folds after CMB-mode exit, conflicting with standard reheating unless the model is retuned or reheating is exotic.
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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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