Primordial black hole abundance from random Gaussian curvature perturbations and a local density threshold

By Chul-Moon Yoo, T. Harada, J. Garriga, K. Kohri. Progress of Theoretical and Experimental Physics, 2018

157 citations recorded by the source corpus.

The production rate of primordial black holes is often calculated by considering a nearly Gaussian distribution of cosmological perturbations, and assuming that black holes will form in regions where the amplitude of such perturbations exceeds a certain threshold. A threshold $\zeta_{\rm th}$ for the curvature perturbation is somewhat inappropriate for this purpose, because it depends significantly on environmental effects, not essential to the local dynamics. By contrast, a threshold $\delta_{\rm th}$ for the density perturbation at horizon crossing seems to provide a more robust criterion. On the other hand, the density perturbation is known to be bounded above by a maximum limit $\delta_{\rm max}$, and given that $\delta_{\rm th}$ is comparable to $\delta_{\rm max}$, the density perturbation will be far from Gaussian near or above the threshold. In this paper, we provide a new plausible estimate for the primordial black hole abundance based on peak theory. In our approach, we assume that the curvature perturbation is given as a random Gaussian field with the power spectrum characterized by a single scale, while an optimized criterion for PBH formation is imposed, based on the locally averaged density perturbation. Both variables are related by the full nonlinear expression derived in the long-wavelength approximation of general relativity. We do not introduce a window function, and the scale of the inhomogeneity is introduced as a random variable in the peak theory. We find that the mass spectrum is shifted to larger mass scales by one order of magnitude or so, compared to a conventional calculation. The abundance of PBHs becomes significantly larger than the conventional one, by many orders of magnitude, mainly due to the optimized criterion for PBH formation and the removal of the suppresion associated with a window function.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b0b23217179c0eaacae580ad8420018039c24db1

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In Astronomy and Astrophysics

1. C. Byrnes
2. S. Young
3. A. Riotto
4. G. Franciolini
5. A. Kehagias
6. I. Musco
7. Marco Peloso
8. V. D. Luca

In Nuclear and High Energy Physics

1. C. Byrnes
2. S. Young
3. I. Musco
4. A. Riotto
5. G. Franciolini
6. A. Kehagias
7. Marco Peloso
8. S. Patil

Citations in the corpus

• Steepest growth of the power spectrum and primordial black holes (2018, background): “More broadly, the general calculation has been questioned recently in [87, 88], with particular uncertainty on”
• Primordial black hole formation and abundance: contribution from the non-linear relation between the density and curvature perturbation (2019, methodology): “In the gradient expansion the non-linear relation between the density contrast δρ/ρb defined on a comoving uniform-cosmic time slicing and the curvature perturbation ζ is given by [23, 25, 29], which is exact up to the first non-zero terms in”
• The ineludible non-Gaussianity of the primordial black hole abundance (2019, methodology): “[7, 8] and do not introduce a window function for the peak theory.”
• Solar-mass primordial black holes explain NANOGrav hint of gravitational waves (2020, unknown): “[53–57] for more rigorous treatments.”