論文

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2018年12月1日

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

Progress of Theoretical and Experimental Physics
  • Chul Moon Yoo
  • ,
  • Tomohiro Harada
  • ,
  • Jaume Garriga
  • ,
  • Kazunori Kohri

2018
12
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1093/ptep/pty120

© The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan. The production rate of primordial black holes (PBHs) 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 ζth 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 δth 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 δmax at the horizon entry and, given that δth is comparable to δmax, 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 around the nearly spherically symmetric high peaks. Both variables are related by the full non-linear expression derived in the long-wavelength approximation of general relativity. We do not introduce a window function, which is usually introduced to obtain the scale dependence of the spectrum. The scale of the inhomogeneity is introduced as a random variable in the peak theory, and the scale-dependent PBH fraction is automatically induced. 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 suppression associated with a window function.

リンク情報
DOI
https://doi.org/10.1093/ptep/pty120
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ID情報
  • DOI : 10.1093/ptep/pty120
  • eISSN : 2050-3911
  • SCOPUS ID : 85062351702

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