The ineludible non-Gaussianity of the primordial black hole abundance

We study the formation of primordial black holes when they are generated by the collapse of large overdensities in the early universe. Since the density contrast is related to the comoving curvature perturbation by a nonlinear relation, the overdensity statistics is unavoidably non-Gaussian. We show...

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Bibliographic Details
Published in:Journal of cosmology and astroparticle physics 2019-07, Vol.2019 (7), p.48-48
Main Authors: Luca, V. De, Franciolini, G., Kehagias, A., Peloso, M., Riotto, A., Ünal, C.
Format: Article
Language:English
Subjects:
Black holes
Flux density
Mathematical analysis
Normal distribution
Perturbation
Power spectra
Probability distribution
Statistics
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Summary:We study the formation of primordial black holes when they are generated by the collapse of large overdensities in the early universe. Since the density contrast is related to the comoving curvature perturbation by a nonlinear relation, the overdensity statistics is unavoidably non-Gaussian. We show that the abundance of primordial black holes at formation may not be captured by a perturbative approach which retains the first few cumulants of the non-Gaussian probability distribution. We provide two techniques to calculate the non-Gaussian abundance of primordial black holes at formation, one based on peak theory and the other on threshold statistics. Our results show that the unavoidable non-Gaussian nature of the inhomogeneities in the energy density makes it harder to generate PBHs. We provide simple (semi-)analytical expressions to calculate the non-Gaussian abundances of the primordial black holes and show that for both narrow and broad power spectra the gaussian case from threshold statistics is reproduced by increasing the amplitude of the power spectrum by a factor (2÷3).
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2019/07/048