Clustering and Runaway Merging in a Primordial Black Hole Dominated Universe

Author(s)

Holst, Ian, Krnjaic, Gordan, Xiao, Huangyu

Abstract

If primordial black holes (PBH) are present in the early universe, their contribution to the energy budget grows relative to that of radiation and generically becomes dominant unless the initial abundance is exponentially small. This black hole domination scenario is largely unconstrained for PBHs with masses $\lesssim 10^9\,\mathrm{g}$, which evaporate prior to Big Bang nucleosynthesis. However, if the era of PBH domination is sufficiently long, the PBHs form clusters and can merge appreciably within these objects. We calculate the population statistics of these clusters within the Press-Schechter formalism and find that, for a wide range of PBH masses and Hubble rates at the onset of PBH domination, the mergers within PBH clusters can exhibit runaway behavior, where the majority of the cluster will eventually form a single black hole with a mass much greater than the original PBH mass. These mergers can dramatically alter the PBH mass distribution and leave behind merged relic black holes that evaporate after Big Bang nucleosynthesis and yield various observational signatures, excluding parameter choices previously thought to be viable

Figures

Example timeline describing the black hole domination scenario. At $t = t_\form$ a subdominant population of PBHs forms during radiation domination in the early universe. Since PBHs redshift like nonrelativistic matter, their energy fraction grows linearly during this era and they dominate the energy budget at $ t = t_i$, which serves as the starting point for our analysis in this paper. During PBH domination, density perturbations grow linearly with scale factor and PBH clusters begin to form. Within a range of cluster masses, PBH mergers can be fast compared to Hubble expansion and consume most of the cluster in a runaway merger. This process forms a sub-population of more massive, longer lived PBH relics which can survive past $t = \tau$ when the original PBH population evaporates due to Hawking emission. Thus, even though the original PBH population evaporates before BBN, the relic population can have important consequences for BBN and CMB observables and may also survive into the later universe. This sequence of events gives rise to gravitational waves from the PBH mergers, the Hawking emission at evaporation, and from second order scalar perturbations.

Example timeline describing the black hole domination scenario. At $t = t_\form$ a subdominant population of PBHs forms during radiation domination in the early universe. Since PBHs redshift like nonrelativistic matter, their energy fraction grows linearly during this era and they dominate the energy budget at $ t = t_i$, which serves as the starting point for our analysis in this paper. During PBH domination, density perturbations grow linearly with scale factor and PBH clusters begin to form. Within a range of cluster masses, PBH mergers can be fast compared to Hubble expansion and consume most of the cluster in a runaway merger. This process forms a sub-population of more massive, longer lived PBH relics which can survive past $t = \tau$ when the original PBH population evaporates due to Hawking emission. Thus, even though the original PBH population evaporates before BBN, the relic population can have important consequences for BBN and CMB observables and may also survive into the later universe. This sequence of events gives rise to gravitational waves from the PBH mergers, the Hawking emission at evaporation, and from second order scalar perturbations.


A summary of important timescales in our scenario for a range of initial cluster sizes $N_i$, for two choices of free parameters $m_i, t_i$. Relevant cosmic events are labeled at the top, including BHD, BBN, CMB, and the present time. The purple~\colorindicator{AA33FF} line gives the cluster size corresponding to the mass contained within the horizon. The green~\colorindicator{119977} curve shows the size of the PBH cluster which can form at a given cosmic time. At a later time, indicated by the dark blue~\colorindicator{223388} runaway merger curve, PBH clusters of a given size collapse and merge to a single BH. Finally, this merged relic evaporates at the time of the blue~\colorindicator{00BBEE} dashed curve. The light blue~\colorindicator{99AAFF} $N_{H,i}$ line divides scales that were sub- and super-horizon at $t_i$.

A summary of important timescales in our scenario for a range of initial cluster sizes $N_i$, for two choices of free parameters $m_i, t_i$. Relevant cosmic events are labeled at the top, including BHD, BBN, CMB, and the present time. The purple~\colorindicator{AA33FF} line gives the cluster size corresponding to the mass contained within the horizon. The green~\colorindicator{119977} curve shows the size of the PBH cluster which can form at a given cosmic time. At a later time, indicated by the dark blue~\colorindicator{223388} runaway merger curve, PBH clusters of a given size collapse and merge to a single BH. Finally, this merged relic evaporates at the time of the blue~\colorindicator{00BBEE} dashed curve. The light blue~\colorindicator{99AAFF} $N_{H,i}$ line divides scales that were sub- and super-horizon at $t_i$.


A summary of important timescales in our scenario for a range of initial cluster sizes $N_i$, for two choices of free parameters $m_i, t_i$. Relevant cosmic events are labeled at the top, including BHD, BBN, CMB, and the present time. The purple~\colorindicator{AA33FF} line gives the cluster size corresponding to the mass contained within the horizon. The green~\colorindicator{119977} curve shows the size of the PBH cluster which can form at a given cosmic time. At a later time, indicated by the dark blue~\colorindicator{223388} runaway merger curve, PBH clusters of a given size collapse and merge to a single BH. Finally, this merged relic evaporates at the time of the blue~\colorindicator{00BBEE} dashed curve. The light blue~\colorindicator{99AAFF} $N_{H,i}$ line divides scales that were sub- and super-horizon at $t_i$.

A summary of important timescales in our scenario for a range of initial cluster sizes $N_i$, for two choices of free parameters $m_i, t_i$. Relevant cosmic events are labeled at the top, including BHD, BBN, CMB, and the present time. The purple~\colorindicator{AA33FF} line gives the cluster size corresponding to the mass contained within the horizon. The green~\colorindicator{119977} curve shows the size of the PBH cluster which can form at a given cosmic time. At a later time, indicated by the dark blue~\colorindicator{223388} runaway merger curve, PBH clusters of a given size collapse and merge to a single BH. Finally, this merged relic evaporates at the time of the blue~\colorindicator{00BBEE} dashed curve. The light blue~\colorindicator{99AAFF} $N_{H,i}$ line divides scales that were sub- and super-horizon at $t_i$.


Average PBH mass as a function of initial cluster PBH number $N_i$ at different times, for two choices of initial parameters $m_i$ and $t_i$. Initially at cluster formation ($t=t_\cl$), the average mass is $m_i$ (green~\colorindicator{119977} line), but eventually some clusters undergo runaway mergers and their average mass grows, finally reaching the mass shown by the dark blue~\colorindicator{223388} line at $t = t_\col$. The red~\colorindicator{FF2244} curve shows the current remaining relic masses after the cosmologically unstable ones have evaporated away by the present day ($t=t_0$). Note that for the parameters on the right, all relics evaporate before the present day. The top panel on either side shows the fractional distribution of PBHs in each cluster size at the time of PBH evaporation $\tau$ in gray~\colorindicator{BBBBCC}.

Average PBH mass as a function of initial cluster PBH number $N_i$ at different times, for two choices of initial parameters $m_i$ and $t_i$. Initially at cluster formation ($t=t_\cl$), the average mass is $m_i$ (green~\colorindicator{119977} line), but eventually some clusters undergo runaway mergers and their average mass grows, finally reaching the mass shown by the dark blue~\colorindicator{223388} line at $t = t_\col$. The red~\colorindicator{FF2244} curve shows the current remaining relic masses after the cosmologically unstable ones have evaporated away by the present day ($t=t_0$). Note that for the parameters on the right, all relics evaporate before the present day. The top panel on either side shows the fractional distribution of PBHs in each cluster size at the time of PBH evaporation $\tau$ in gray~\colorindicator{BBBBCC}.


Average PBH mass as a function of initial cluster PBH number $N_i$ at different times, for two choices of initial parameters $m_i$ and $t_i$. Initially at cluster formation ($t=t_\cl$), the average mass is $m_i$ (green~\colorindicator{119977} line), but eventually some clusters undergo runaway mergers and their average mass grows, finally reaching the mass shown by the dark blue~\colorindicator{223388} line at $t = t_\col$. The red~\colorindicator{FF2244} curve shows the current remaining relic masses after the cosmologically unstable ones have evaporated away by the present day ($t=t_0$). Note that for the parameters on the right, all relics evaporate before the present day. The top panel on either side shows the fractional distribution of PBHs in each cluster size at the time of PBH evaporation $\tau$ in gray~\colorindicator{BBBBCC}.

Average PBH mass as a function of initial cluster PBH number $N_i$ at different times, for two choices of initial parameters $m_i$ and $t_i$. Initially at cluster formation ($t=t_\cl$), the average mass is $m_i$ (green~\colorindicator{119977} line), but eventually some clusters undergo runaway mergers and their average mass grows, finally reaching the mass shown by the dark blue~\colorindicator{223388} line at $t = t_\col$. The red~\colorindicator{FF2244} curve shows the current remaining relic masses after the cosmologically unstable ones have evaporated away by the present day ($t=t_0$). Note that for the parameters on the right, all relics evaporate before the present day. The top panel on either side shows the fractional distribution of PBHs in each cluster size at the time of PBH evaporation $\tau$ in gray~\colorindicator{BBBBCC}.


The mass function of merged relic PBHs for two choices of free parameters. Initially, all the PBHs have the same mass $m_i$, shown in green~\colorindicator{119977}. The blue~\colorindicator{223388} and red~\colorindicator{FF2244} curves show the initial and present-day mass functions of merged relics, which clearly shows the mass growth from runaway mergers. Superimposed in blue~\colorindicator{00BBEE} are observational bounds on evaporating BHs from BBN \cite{CarrConstraintsPBHs2021}, CMB \cite{AcharyaCMBBBNConstraints2020}, the extragalactic gamma-ray background (EGB) \cite{CarrConstraintsPBHs2021} and Voyager $e^\pm$ \cite{Boudaud:2018hqb}. Both choices of PBH parameters are ruled out by observations because they produce too many evaporating relic BHs, particularly during BBN or CMB emission. Note that the plot visually compares limits on $f_\BH$ to the logarithmic mass distribution $df_\BH / d \log m$, but the proper comparison is made with \Eq{eq:fBHlimit}.

The mass function of merged relic PBHs for two choices of free parameters. Initially, all the PBHs have the same mass $m_i$, shown in green~\colorindicator{119977}. The blue~\colorindicator{223388} and red~\colorindicator{FF2244} curves show the initial and present-day mass functions of merged relics, which clearly shows the mass growth from runaway mergers. Superimposed in blue~\colorindicator{00BBEE} are observational bounds on evaporating BHs from BBN \cite{CarrConstraintsPBHs2021}, CMB \cite{AcharyaCMBBBNConstraints2020}, the extragalactic gamma-ray background (EGB) \cite{CarrConstraintsPBHs2021} and Voyager $e^\pm$ \cite{Boudaud:2018hqb}. Both choices of PBH parameters are ruled out by observations because they produce too many evaporating relic BHs, particularly during BBN or CMB emission. Note that the plot visually compares limits on $f_\BH$ to the logarithmic mass distribution $df_\BH / d \log m$, but the proper comparison is made with \Eq{eq:fBHlimit}.


The mass function of merged relic PBHs for two choices of free parameters. Initially, all the PBHs have the same mass $m_i$, shown in green~\colorindicator{119977}. The blue~\colorindicator{223388} and red~\colorindicator{FF2244} curves show the initial and present-day mass functions of merged relics, which clearly shows the mass growth from runaway mergers. Superimposed in blue~\colorindicator{00BBEE} are observational bounds on evaporating BHs from BBN \cite{CarrConstraintsPBHs2021}, CMB \cite{AcharyaCMBBBNConstraints2020}, the extragalactic gamma-ray background (EGB) \cite{CarrConstraintsPBHs2021} and Voyager $e^\pm$ \cite{Boudaud:2018hqb}. Both choices of PBH parameters are ruled out by observations because they produce too many evaporating relic BHs, particularly during BBN or CMB emission. Note that the plot visually compares limits on $f_\BH$ to the logarithmic mass distribution $df_\BH / d \log m$, but the proper comparison is made with \Eq{eq:fBHlimit}.

The mass function of merged relic PBHs for two choices of free parameters. Initially, all the PBHs have the same mass $m_i$, shown in green~\colorindicator{119977}. The blue~\colorindicator{223388} and red~\colorindicator{FF2244} curves show the initial and present-day mass functions of merged relics, which clearly shows the mass growth from runaway mergers. Superimposed in blue~\colorindicator{00BBEE} are observational bounds on evaporating BHs from BBN \cite{CarrConstraintsPBHs2021}, CMB \cite{AcharyaCMBBBNConstraints2020}, the extragalactic gamma-ray background (EGB) \cite{CarrConstraintsPBHs2021} and Voyager $e^\pm$ \cite{Boudaud:2018hqb}. Both choices of PBH parameters are ruled out by observations because they produce too many evaporating relic BHs, particularly during BBN or CMB emission. Note that the plot visually compares limits on $f_\BH$ to the logarithmic mass distribution $df_\BH / d \log m$, but the proper comparison is made with \Eq{eq:fBHlimit}.


In this set of plots, we present the $(m_i, t_i)$ parameter space of PBH domination, and various phenomenological results. The gray regions are not physically viable as the PBHs either evaporate before initial domination or have an initial mass larger than the horizon mass. Elsewhere, the parameter space allows for BH domination and clustering. We present different information on different plots. On the upper left, we plot the parameter space ruled out by observational bounds on Hawking evaporation from the relics that form for a given $m_i$, $t_i$ combination. On the upper right, we present contours of the maximum mass of the final merged PBH relics. On the lower left, we plot the relic BH density compared to the dark matter density ($f_\BH$) at $t = \tau$, just after the original PBH population evaporates and only the relics are left. Accounting for the evaporation of BHs, on the lower right we plot $f_\BH$ of merged relics at the present time.

In this set of plots, we present the $(m_i, t_i)$ parameter space of PBH domination, and various phenomenological results. The gray regions are not physically viable as the PBHs either evaporate before initial domination or have an initial mass larger than the horizon mass. Elsewhere, the parameter space allows for BH domination and clustering. We present different information on different plots. On the upper left, we plot the parameter space ruled out by observational bounds on Hawking evaporation from the relics that form for a given $m_i$, $t_i$ combination. On the upper right, we present contours of the maximum mass of the final merged PBH relics. On the lower left, we plot the relic BH density compared to the dark matter density ($f_\BH$) at $t = \tau$, just after the original PBH population evaporates and only the relics are left. Accounting for the evaporation of BHs, on the lower right we plot $f_\BH$ of merged relics at the present time.


In this set of plots, we present the $(m_i, t_i)$ parameter space of PBH domination, and various phenomenological results. The gray regions are not physically viable as the PBHs either evaporate before initial domination or have an initial mass larger than the horizon mass. Elsewhere, the parameter space allows for BH domination and clustering. We present different information on different plots. On the upper left, we plot the parameter space ruled out by observational bounds on Hawking evaporation from the relics that form for a given $m_i$, $t_i$ combination. On the upper right, we present contours of the maximum mass of the final merged PBH relics. On the lower left, we plot the relic BH density compared to the dark matter density ($f_\BH$) at $t = \tau$, just after the original PBH population evaporates and only the relics are left. Accounting for the evaporation of BHs, on the lower right we plot $f_\BH$ of merged relics at the present time.

In this set of plots, we present the $(m_i, t_i)$ parameter space of PBH domination, and various phenomenological results. The gray regions are not physically viable as the PBHs either evaporate before initial domination or have an initial mass larger than the horizon mass. Elsewhere, the parameter space allows for BH domination and clustering. We present different information on different plots. On the upper left, we plot the parameter space ruled out by observational bounds on Hawking evaporation from the relics that form for a given $m_i$, $t_i$ combination. On the upper right, we present contours of the maximum mass of the final merged PBH relics. On the lower left, we plot the relic BH density compared to the dark matter density ($f_\BH$) at $t = \tau$, just after the original PBH population evaporates and only the relics are left. Accounting for the evaporation of BHs, on the lower right we plot $f_\BH$ of merged relics at the present time.


In this set of plots, we present the $(m_i, t_i)$ parameter space of PBH domination, and various phenomenological results. The gray regions are not physically viable as the PBHs either evaporate before initial domination or have an initial mass larger than the horizon mass. Elsewhere, the parameter space allows for BH domination and clustering. We present different information on different plots. On the upper left, we plot the parameter space ruled out by observational bounds on Hawking evaporation from the relics that form for a given $m_i$, $t_i$ combination. On the upper right, we present contours of the maximum mass of the final merged PBH relics. On the lower left, we plot the relic BH density compared to the dark matter density ($f_\BH$) at $t = \tau$, just after the original PBH population evaporates and only the relics are left. Accounting for the evaporation of BHs, on the lower right we plot $f_\BH$ of merged relics at the present time.

In this set of plots, we present the $(m_i, t_i)$ parameter space of PBH domination, and various phenomenological results. The gray regions are not physically viable as the PBHs either evaporate before initial domination or have an initial mass larger than the horizon mass. Elsewhere, the parameter space allows for BH domination and clustering. We present different information on different plots. On the upper left, we plot the parameter space ruled out by observational bounds on Hawking evaporation from the relics that form for a given $m_i$, $t_i$ combination. On the upper right, we present contours of the maximum mass of the final merged PBH relics. On the lower left, we plot the relic BH density compared to the dark matter density ($f_\BH$) at $t = \tau$, just after the original PBH population evaporates and only the relics are left. Accounting for the evaporation of BHs, on the lower right we plot $f_\BH$ of merged relics at the present time.


In this set of plots, we present the $(m_i, t_i)$ parameter space of PBH domination, and various phenomenological results. The gray regions are not physically viable as the PBHs either evaporate before initial domination or have an initial mass larger than the horizon mass. Elsewhere, the parameter space allows for BH domination and clustering. We present different information on different plots. On the upper left, we plot the parameter space ruled out by observational bounds on Hawking evaporation from the relics that form for a given $m_i$, $t_i$ combination. On the upper right, we present contours of the maximum mass of the final merged PBH relics. On the lower left, we plot the relic BH density compared to the dark matter density ($f_\BH$) at $t = \tau$, just after the original PBH population evaporates and only the relics are left. Accounting for the evaporation of BHs, on the lower right we plot $f_\BH$ of merged relics at the present time.

In this set of plots, we present the $(m_i, t_i)$ parameter space of PBH domination, and various phenomenological results. The gray regions are not physically viable as the PBHs either evaporate before initial domination or have an initial mass larger than the horizon mass. Elsewhere, the parameter space allows for BH domination and clustering. We present different information on different plots. On the upper left, we plot the parameter space ruled out by observational bounds on Hawking evaporation from the relics that form for a given $m_i$, $t_i$ combination. On the upper right, we present contours of the maximum mass of the final merged PBH relics. On the lower left, we plot the relic BH density compared to the dark matter density ($f_\BH$) at $t = \tau$, just after the original PBH population evaporates and only the relics are left. Accounting for the evaporation of BHs, on the lower right we plot $f_\BH$ of merged relics at the present time.


References
  • [1] S. Hawking, “Gravitationally collapsed objects of very low mass,” Mon. Not. Roy. Astron. Soc. 152 (Jan., 1971) 75.
  • [2] M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, “Primordial black holes—perspectives in gravitational wave astronomy,” Class. Quantum Gravity 35 no. 6, (2018) 063001, arXiv:1801.05235 [astro-ph.CO].
  • [3] B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, “Constraints on primordial black holes,” Rept. Prog. Phys. 84 no. 11, (2021) 116902, arXiv:2002.12778 [astro-ph.CO].
  • [4] A. M. Green and B. J. Kavanagh, “Primordial black holes as a dark matter candidate,” J. Phys. G: Nucl. Part. Phys. 48 no. 4, (2021) 043001, arXiv:2007.10722 [astro-ph.CO].
  • [5] S. K. Acharya and R. Khatri, “CMB and BBN constraints on evaporating primordial black holes revisited,” JCAP 06 (2020) 018, arXiv:2002.00898 [astro-ph.CO].
  • [6] D. Hooper, G. Krnjaic, and S. D. McDermott, “Dark radiation and superheavy dark matter from black hole domination,” JHEP 2019 no. 8, (2019), arXiv:1905.01301 [hep-ph].
  • [7] M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, “Primordial Black Hole Scenario for the Gravitational-Wave Event GW150914,” PRL 117 no. 6, (2016), arXiv:1603.08338 [astro-ph.CO].
  • [8] M. Raidal, V. Vaskonen, and H. Veermäe, “Gravitational waves from primordial black hole mergers,” JCAP 2017 no. 09, (2017) 037–037, arXiv:1707.01480 [astro-ph.CO].
  • [9] J. L. Zagorac, R. Easther, and N. Padmanabhan, “GUT-scale primordial black holes: mergers and gravitational waves,” JCAP 2019 no. 06, (2019) 052–052, arXiv:1903.05053 [astro-ph.CO].
  • [10] D. Hooper, G. Krnjaic, J. March-Russell, S. D. McDermott, and R. Petrossian-Byrne, “Hot Gravitons and Gravitational Waves From Kerr Black Holes in the Early Universe,” arXiv:2004.00618 [astro-ph.CO].
  • [11] C. J. Shallue, J. B. Muñoz, and G. Z. Krnjaic, “Warm Hawking Relics From Primordial Black Hole Domination,” arXiv:2406.08535 [astro-ph.CO].
  • [12] D. Baumann, P. J. Steinhardt, and N. Turok, “Primordial Black Hole Baryogenesis,” arXiv:hep-th/0703250.
  • [13] L. Morrison, S. Profumo, and Y. Yu, “Melanopogenesis: dark matter of (almost) any mass and baryonic matter from the evaporation of primordial black holes weighing a ton (or less),” JCAP 2019 no. 05, (2019) 005–005, arXiv:1812.10606 [astro-ph.CO].
  • [14] D. Hooper and G. Krnjaic, “GUT baryogenesis with primordial black holes,” PRD 103 no. 4, (2021), arXiv:2010.01134 [hep-ph].
  • [15] N. Bernal, C. S. Fong, Y. F. Perez-Gonzalez, and J. Turner, “Rescuing high-scale leptogenesis using primordial black holes,” Phys. Rev. D 106 no. 3, (2022) 035019, arXiv:2203.08823 [hep-ph].
  • [16] O. Lennon, J. March-Russell, R. Petrossian-Byrne, and H. Tillim, “Black hole genesis of dark matter,” JCAP 2018 no. 04, (2018) 009–009, arXiv:1712.07664 [hep-ph].
  • [17] A. Cheek, L. Heurtier, Y. F. Perez-Gonzalez, and J. Turner, “Primordial black hole evaporation and dark matter production. I. Solely Hawking radiation,” Phys. Rev. D 105 no. 1, (2022) 015022, arXiv:2107.00013 [hep-ph].
  • [18] R. Allahverdi, M. A. Amin, et al., “The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe,” Open J. Astrophys. 4 no. 1, (2021), arXiv:2006.16182 [astro-ph.CO].
  • [19] W. H. Press and P. Schechter, “Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation,” ApJ 187 (1974) 425.
  • [20] M. Fishbach, D. E. Holz, and B. Farr, “Are LIGO’s Black Holes Made from Smaller Black Holes?,” ApJL 840 no. 2, (2017) L24, arXiv:1703.06869 [astro-ph.HE].
  • [21] V. D. Luca, V. Desjacques, G. Franciolini, and A. Riotto, “The clustering evolution of primordial black holes,” JCAP 2020 no. 11, (2020) 028–028, arXiv:2009.04731 [astro-ph.CO].
  • [22] G. Franciolini, K. Kritos, E. Berti, and J. Silk, “Primordial black hole mergers from three-body interactions,” PRD 106 no. 8, (2022), arXiv:2205.15340 [astro-ph.CO].
  • [23] M. S. Delos, A. Rantala, S. Young, and F. Schmidt, “Structure formation with primordial black holes: collisional dynamics, binaries, and gravitational waves,” arXiv:2410.01876 [astro-ph.CO].
  • [24] T. Nakamura, M. Sasaki, T. Tanaka, and K. S. Thorne, “Gravitational Waves from Coalescing Black Hole MACHO Binaries,” ApJ 487 no. 2, (1997) L139–L142, arXiv:astro-ph/9708060.
  • [25] K. Ioka, T. Chiba, T. Tanaka, and T. Nakamura, “Black hole binary formation in the expanding universe: Three body problem approximation,” PRD 58 no. 6, (1998), arXiv:astro-ph/9807018.
  • [26] Y. Ali-Haı̈moud, E. D. Kovetz, and M. Kamionkowski, “Merger rate of primordial black-hole binaries,” PRD 96 no. 12, (2017), arXiv:1709.06576 [astro-ph.CO].
  • [27] M. Raidal, C. Spethmann, V. Vaskonen, and H. Veermäe, “Formation and evolution of primordial black hole binaries in the early universe,” JCAP 2019 no. 02, (2019) 018–018, arXiv:1812.01930 [astro-ph.CO].
  • [28] V. De Luca, G. Franciolini, and A. Riotto, “Heavy Primordial Black Holes from Strongly Clustered Light Black Holes,” PRL 130 no. 17, (2023), arXiv:2210.14171 [astro-ph.CO].
  • [29] J. R. Chisholm, “Clustering of Primordial Black Holes. II. Evolution of Bound Systems,” Phys. Rev. D 84 (2011) 124031, arXiv:1110.4402 [astro-ph.CO].
  • [30] T. Kim and P. Lu, “Primordial Black Hole Reformation in the Early Universe,” arXiv:2411.07469 [astro-ph.CO].
  • [31] G. Xu and J. P. Ostriker, “Dynamics of massive black holes as a possible candidate of Galactic dark matter,” ApJ 437 (1994) 184.
  • [32] T. Tanaka and Z. Haiman, “The Assembly of Supermassive Black Holes at High Redshifts,” Astrophys. J. 696 (2009) 1798–1822, arXiv:0807.4702 [astro-ph].
  • [33] K. Inayoshi, E. Visbal, and Z. Haiman, “The Assembly of the First Massive Black Holes,” Ann. Rev. Astron. Astrophys. 58 (2020) 27–97, arXiv:1911.05791 [astro-ph.GA].
  • [34] S. W. Hawking, “Black hole explosions?,” Nature 248 no. 5443, (1974) 30–31.
  • [35] S. W. Hawking, “Particle Creation by Black Holes,” Commun. Math. Phys. 43 (1975) 199–220.
  • [36] J. H. MacGibbon and B. R. Webber, “Quark- and gluon-jet emission from primordial black holes: The instantaneous spectra,” Phys. Rev. D 41 (1990) 3052–3079.
  • [37] J. H. MacGibbon, “Quark and gluon jet emission from primordial black holes. 2. The Lifetime emission,” Phys. Rev. D 44 (1991) 376–392.
  • [38] J. Liu, L. Bian, R.-G. Cai, Z.-K. Guo, and S.-J. Wang, “Primordial black hole production during first-order phase transitions,” PRD 105 no. 2, (2022), arXiv:2106.05637 [astro-ph.CO].
  • [39] S. G. Rubin, M. Y. Khlopov, and A. S. Sakharov, “Primordial black holes from nonequilibrium second order phase transition,” Grav. Cosmol. 6 (2000) 51–58, arXiv:hep-ph/0005271.
  • [40] D. I. Dunsky and M. Kongsore, “Primordial black holes from axion domain wall collapse,” JHEP 06 (2024) 198, arXiv:2402.03426 [hep-ph].
  • [41] E. Cotner and A. Kusenko, “Primordial Black Holes from Supersymmetry in the Early Universe,” PRL 119 no. 3, (2017), arXiv:1612.02529 [astro-ph.CO].
  • [42] Y. Lu, Z. S. C. Picker, S. Profumo, and A. Kusenko, “Black Holes from Fermi Ball Collapse,” arXiv:2411.17074 [astro-ph.CO].
  • [43] T. W. B. Kibble, “Topology of cosmic domains and strings,” J. Phys. A: Math. Gen. 9 no. 8, (1976) 1387–1398.
  • [44] A. Vilenkin, Y. Levin, and A. Gruzinov, “Cosmic strings and primordial black holes,” JCAP 2018 no. 11, (2018) 008–008, arXiv:1808.00670 [astro-ph.CO].
  • [45] M. M. Flores, Y. Lu, and A. Kusenko, “Structure formation after reheating: Supermassive primordial black holes and Fermi ball dark matter,” Phys. Rev. D 108 no. 12, (2023) 123511, arXiv:2308.09094 [astro-ph.CO].
  • [46] J. Bramante, C. V. Cappiello, M. Diamond, J. L. Kim, Q. Liu, and A. C. Vincent, “Dissipative dark cosmology: From early matter dominance to delayed compact objects,” Phys. Rev. D 110 no. 4, (2024) 043041, arXiv:2405.04575 [hep-ph].
  • [47] P. Ralegankar, D. Perri, and T. Kobayashi, “Gravothermalizing into primordial black holes, boson stars, and cannibal stars,” arXiv:2410.18948 [astro-ph.CO].
  • [48] Particle Data Group Collaboration, R. L. Workman, V. D. Burkert, et al., “Review of Particle Physics,” PTEP 2022 no. 8, (2022).
  • [49] V. Desjacques and A. Riotto, “Spatial clustering of primordial black holes,” PRD 98 no. 12, (2018), arXiv:1806.10414 [astro-ph.CO].
  • [50] D. Inman and Y. Ali-Haı̈moud, “Early structure formation in primordial black hole cosmologies,” PRD 100 no. 8, (2019), arXiv:1907.08129 [astro-ph.CO].
  • [51] G. Domènech, V. Takhistov, and M. Sasaki, “Exploring evaporating primordial black holes with gravitational waves,” Phys. Lett. B 823 (2021) 136722, arXiv:2105.06816 [astro-ph.CO].
  • [52] P. Auclair and B. Blachier, “Small-scale clustering of Primordial Black Holes: cloud-in-cloud and exclusion effects,” arXiv:2402.00600 [astro-ph.CO].
  • [53] S. Dodelson, Modern Cosmology. Academic Press, Amsterdam, 2003.
  • [54] A. Cooray and R. K. Sheth, “Halo Models of Large Scale Structure,” Phys. Rept. 372 (2002) 1–129, arXiv:astro-ph/0206508.
  • [55] H. Mo, F. C. van den Bosch, and S. White, Galaxy Formation and Evolution. Cambridge University Press, 2010.
  • [56] J. Binney and S. Tremaine, Galactic Dynamics. Princeton University Press, 1988.
  • [57] C. Blanco, M. S. Delos, A. L. Erickcek, and D. Hooper, “Annihilation signatures of hidden sector dark matter within early-forming microhalos,” PRD 100 no. 10, (2019), arXiv:1906.00010 [astro-ph.CO].
  • [58] H. Xiao, I. Williams, and M. McQuinn, “Simulations of axion minihalos,” PRD 104 no. 2, (2021), arXiv:2101.04177 [astro-ph.CO].
  • [59] I. Cholis, E. D. Kovetz, Y. Ali-Haı̈moud, S. Bird, M. Kamionkowski, J. B. Muñoz, and A. Raccanelli, “Orbital eccentricities in primordial black hole binaries,” PRD 94 no. 8, (2016), arXiv:1606.07437 [astro-ph.HE].
  • [60] A. P. Lightman and S. L. Shapiro, “The dynamical evolution of globular clusters,” Rev. Mod. Phys. 50 no. 2, (1978) 437–481.
  • [61] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation. W. H. Freeman, San Francisco, 1973.
  • [62] M. Turner, “Gravitational radiation from point-masses in unbound orbits - Newtonian results,” ApJ 216 (1977) 610.
  • [63] G. D. Quinlan and S. L. Shapiro, “Dynamical evolution of dense clusters of compact stars,” ApJ 343 (1989) 725.
  • [64] M. H. Lee, “N-Body Evolution of Dense Clusters of Compact Stars,” ApJ 418 (1993) 147.
  • [65] R. M. O’Leary, B. Kocsis, and A. Loeb, “Gravitational waves from scattering of stellar-mass black holes in galactic nuclei,” MNRAS 395 no. 4, (2009) 2127–2146, arXiv:0807.2638 [astro-ph].
  • [66] P. C. Peters, “Gravitational Radiation and the Motion of Two Point Masses,” Phys. Rev. 136 no. 4B, (1964) B1224–B1232.
  • [67] S. Bird, I. Cholis, J. B. Muñoz, Y. Ali-Haı̈moud, M. Kamionkowski, E. D. Kovetz, A. Raccanelli, and A. G. Riess, “Did LIGO detect dark matter?,” Phys. Rev. Lett. 116 no. 20, (2016) 201301, arXiv:1603.00464 [astro-ph.CO].
  • [68] N. Afshordi, P. McDonald, and D. N. Spergel, “Primordial Black Holes as Dark Matter: The Power Spectrum and Evaporation of Early Structures,” ApJ 594 no. 2, (2003) L71–L74, arXiv:astro-ph/0302035.
  • [69] M. Celoria, R. Oliveri, A. Sesana, and M. Mapelli, “Lecture notes on black hole binary astrophysics,” arXiv:1807.11489 [astro-ph.GA].
  • [70] V. A. Ambartsumian, “On the dynamics of open clusters,” Ann. Leningrad State Univ. 22 (1938) 19.
  • [71] L. Spitzer and H. Shapley, “The Stability of Isolated Clusters,” MNRAS 100 no. 5, (1940) 396–413.
  • [72] S. Chandrasekhar, “Dynamical Friction. III. a More Exact Theory of the Rate of Escape of Stars from Clusters.,” ApJ 98 (1943) 54.
  • [73] LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett. 116 no. 6, (2016) 061102, arXiv:1602.03837 [gr-qc].
  • [74] D. Lynden-Bell, R. Wood, and A. Royal, “The Gravo-Thermal Catastrophe in Isothermal Spheres and the Onset of Red-Giant Structure for Stellar Systems,” Mon. Not. Roy. Astron. Soc. 138 no. 4, (1968) 495–525.
  • [75] S. Balberg, S. L. Shapiro, and S. Inagaki, “Selfinteracting dark matter halos and the gravothermal catastrophe,” Astrophys. J. 568 (2002) 475–487, arXiv:astro-ph/0110561.
  • [76] M. Boudaud and M. Cirelli, “Voyager 1 e± Further Constrain Primordial Black Holes as Dark Matter,” Phys. Rev. Lett. 122 no. 4, (2019) 041104, arXiv:1807.03075 [astro-ph.HE].
  • [77] B. J. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, “New cosmological constraints on primordial black holes,” Phys. Rev. D 81 (2010) 104019, arXiv:0912.5297 [astro-ph.CO].
  • [78] N. Bellomo, J. L. Bernal, A. Raccanelli, and L. Verde, “Primordial black holes as dark matter: converting constraints from monochromatic to extended mass distributions,” JCAP 2018 no. 01, (2018) 004–004, arXiv:1709.07467 [astro-ph.CO].
  • [79] CMB-S4 Collaboration, K. N. Abazajian et al., “CMB-S4 Science Book, First Edition,” arXiv:1610.02743 [astro-ph.CO].
  • [80] E. E. Flanagan and S. A. Hughes, “Measuring gravitational waves from binary black hole coalescences: 1. Signal-to-noise for inspiral, merger, and ringdown,” Phys. Rev. D 57 (1998) 4535–4565, arXiv:gr-qc/9701039.
  • [81] P. Ajith et al., “Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins,” Phys. Rev. Lett. 106 (2011) 241101, arXiv:0909.2867 [gr-qc].
  • [82] N. Seto, S. Kawamura, and T. Nakamura, “Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer gravitational wave antenna in space,” Phys. Rev. Lett. 87 (2001) 221103, arXiv:astro-ph/0108011.
  • [83] K. Yagi and N. Seto, “Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries,” Phys. Rev. D 83 (2011) 044011, arXiv:1101.3940 [astro-ph.CO].
  • [84] A. Cheek, L. Heurtier, Y. F. Perez-Gonzalez, and J. Turner, “Redshift effects in particle production from Kerr primordial black holes,” PRD 106 no. 10, (2022), arXiv:2207.09462 [astro-ph.CO].
  • [85] A. Cheek, L. Heurtier, Y. F. Perez-Gonzalez, and J. Turner, “Evaporation of primordial black holes in the early Universe: Mass and spin distributions,” PRD 108 no. 1, (2023), arXiv:2212.03878 [hep-ph].
  • [86] T. Papanikolaou, V. Vennin, and D. Langlois, “Gravitational waves from a universe filled with primordial black holes,” JCAP 2021 no. 03, (2021) 053, arXiv:2010.11573 [astro-ph.CO].
  • [87] D. Baumann, P. Steinhardt, K. Takahashi, and K. Ichiki, “Gravitational wave spectrum induced by primordial scalar perturbations,” PRD 76 no. 8, (2007), arXiv:hep-th/0703290.
  • [88] G. Domènech, C. Lin, and M. Sasaki, “Gravitational wave constraints on the primordial black hole dominated early universe,” JCAP 2021 no. 04, (2021) 062, arXiv:2012.08151 [gr-qc].
  • [89] B. Eggemeier, J. C. Niemeyer, K. Jedamzik, and R. Easther, “Stochastic gravitational waves from postinflationary structure formation,” PRD 107 no. 4, (2023), arXiv:2212.00425 [astro-ph.CO].
  • [90] R. Ebadi, S. Kumar, A. McCune, H. Tai, and L.-T. Wang, “Gravitational waves from stochastic scalar fluctuations,” Phys. Rev. D 109 no. 8, (2024) 083519, arXiv:2307.01248 [astro-ph.CO].
  • [91] G. Domenech, “Scalar Induced Gravitational Waves Review,” Universe 7 no. 11, (2021) 398, arXiv:2109.01398 [gr-qc].
  • [92] N. Fernandez, J. W. Foster, B. Lillard, and J. Shelton, “Stochastic Gravitational Waves from Early Structure Formation,” Phys. Rev. Lett. 133 no. 11, (2024) 111002, arXiv:2312.12499 [astro-ph.CO].
  • [93] K. Inomata, K. Kohri, T. Nakama, and T. Terada, “Enhancement of gravitational waves induced by scalar perturbations due to a sudden transition from an early matter era to the radiation era,” PRD 100 no. 4, (2019), arXiv:1904.12879 [astro-ph.CO].
  • [94] K. Inomata, M. Kawasaki, K. Mukaida, T. Terada, and T. T. Yanagida, “Gravitational wave production right after a primordial black hole evaporation,” PRD 101 no. 12, (2020), arXiv:2003.10455 [astro-ph.CO].