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Primordial black hole mass functions as a probe of cosmic origin

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Abstract

We discuss a novel window to probe the origin of our universe via the mass functions of primordial black holes (PBHs). The mass functions of PBHs are simply estimated using the conventional Press-Schechter formalism for two paradigms of cosmic origin, including inflationary ΛCDM and bounce cosmology. The standard inflationary ΛCDM model cannot generate an appreciable number of massive PBHs; however, non-trivial inflation models with blue-tilted power spectra at small scales and matter bounce cosmology provide formation mechanisms for heavy PBHs, which in turn, may seed the observed supermassive black holes (SMBHs). By fitting the SMBH mass functions at high redshift (z ∼ 6) derived from Sloan Digital Sky Survey (SDSS) and Canada-France High-z Quasar Survey (CFHQS) quasars, for two paradigms of cosmic origin, we derive constraints on the PBH density fraction fPBH at z ∼ 6 and the characteristic mass M⋆, with the prior assumption that all SMBHs stem from PBHs. We demonstrate that this newly proposed procedure, relying on astronomical measurements that utilize deep-field surveys of SMBHs at high redshift, can be used to constrain models of cosmic origin. Additionally, although not the main focus of this paper, we evolve the mass function from z ∼ 6 to z ∼ 0 through an assumption of 3 × 108-year Eddington’s accretion, and give a rough estimation of fPBH at z ∼ 0.

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Authors and Affiliations

  1. Deep Space Exploration Laboratory/School of Physical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Yi-Fu Cai, Chengfeng Tang, Geyu Mo, Xiao-Han Ma, Bo Wang & Wentao Luo

  2. CAS Key Laboratory for Researches in Galaxies and Cosmology/Department of Astronomy, School of Astronomy and Space Science, University of Science and Technology of China, Hefei, 230026, China

    Yi-Fu Cai, Chengfeng Tang, Geyu Mo, Xiao-Han Ma, Bo Wang & Wentao Luo

  3. Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Milano, Milano, 20146, Italy

    Sheng-Feng Yan

  4. DiSAT, Università degli Studi dell’Insubria, Como, 22100, Italy

    Sheng-Feng Yan

  5. Jockey Club Institute for Advanced Study, The Hong Kong University of Science and Technology, Hong Kong, China

    Chao Chen

  6. Department of Physics, Arizona State University, Tempe, 85287-1504, USA

    Damien A. Easson

  7. Department of Physics & Center for Field Theory and Particle Physics, Fudan University, Shanghai, 200433, China

    Antonino Marcianò

  8. Laboratori Nazionali di Frascati INFN, Via Enrico Fermi 54, Frascati (Roma), 00044, Italy

    Antonino Marcianò

  9. INFN sezione Roma Tor Vergata, Rome, I-00133, Italy

    Antonino Marcianò

  10. School of Physics, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Sheng-Feng Yan

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  1. Yi-Fu Cai
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  2. Chengfeng Tang
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  3. Geyu Mo
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  4. Sheng-Feng Yan
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  5. Chao Chen
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  6. Xiao-Han Ma
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  7. Bo Wang
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  9. Damien A. Easson
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  10. Antonino Marcianò
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Corresponding authors

Correspondence to Yi-Fu Cai, Bo Wang, Damien A. Easson or Antonino Marcianò.

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Conflict of interest The authors declare that they have no conflict of interest.

Additional information

We are grateful to Bernard Carr, Yun Fang, Ricardo Z. Ferreira, Amara Ilyas, Ugo Moschella, Jerome Quintin, Misao Sasaki, Dong-Gang Wang, Yi Wang, Zihan Zhou, and Mian Zhu for valuable communications. This work was supported in part by the National Key R&D Program of China (Grant No. 2021YFC2203100), CAS Young Interdisciplinary Innovation Team (Grant No. JCTD-2022-20), National Natural Science Foundation of China (Grant Nos. 11875113, 11961131007, 12261131497, 12003029, 11833005, and 12192224), 111 Project for “Observational and Theoretical Research on Dark Matter and Dark Energy” (Grant No. B23042), Fundamental Research Funds for Central Universities, CSC Innovation Talent Funds, USTC Fellowship for International Cooperation, USTC Research Funds of the Double First-Class Initiative, CAS project for young scientists in basic research (Grant No. YSBR-006), Shanghai Municipality Science and Technology Commission (Grant No. KBH1512299). Sheng-Feng Yan is supported by the Disposizione del Presidente INFN n. 24433 in INFN Sezione di Milano. Damien A. Easson is supported in part by the U.S. Department of Energy, Office of High Energy Physics (Grant No. DE-SC0019470), and the Foundational Questions Institute (Grant No. FQXi-MGB-1927). We acknowledge the use of the computing cluster LINDA & JUDY in the particle cosmology group at USTC.

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Cai, YF., Tang, C., Mo, G. et al. Primordial black hole mass functions as a probe of cosmic origin. Sci. China Phys. Mech. Astron. 67, 259512 (2024). https://doi.org/10.1007/s11433-023-2314-1

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