Physics of the Dark Universe 36 (2022) 101009 Contents lists available at ScienceDirect Physics of the Dark Universe journal homepage: www.elsevier.com/locate/dark The stochastic gravitational wave background from close hyperbolic encounters of primordial black holes in dense clusters Juan García-Bellido a,∗ , Santiago Jaraba a , Sachiko Kuroyanagi a,b a Instituto de Física Teórica UAM-CSIC, Universidad Autonóma de Madrid, Cantoblanco 28049 Madrid, Spain b Department of Physics and Astrophysics, Nagoya University, Nagoya, 464-8602, Japan article info Article history: Received 13 January 2022 Received in revised form 16 March 2022 Accepted 24 March 2022 Keywords: Stochastic background Gravitational waves Primordial black holes Hyperbolic encounters abstract The inner part of dense clusters of primordial black holes is an active environment where multiple scattering processes take place. Some of them give rise from time to time to bounded pairs, and the rest ends up with a single scattering event. The former eventually evolves to a binary black hole (BBH) emitting periodic gravitational waves (GWs), while the latter with a short distance, called close hyperbolic encounters (CHE), emits a strong GW burst. We make the first calculation of the stochastic GW background originating from unresolved CHE sources. Unlike the case for BBH, the low-frequency tail of the SGWB from CHE is sensitive to the redshift dependence of the event rate, which could help distinguish the astrophysical from the primordial black hole contributions. We find that there is a chance that CHE can be tested by third-generation ground-based GW detectors such as Einstein Telescope and Cosmic Explorer. © 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction Primordial black holes (PBHs) may have formed in the early Universe [1–5]. They can be formed by the gravitational collapse of overdense regions, caused by high peaks in the primordial cur- vature power spectrum generated during inflation [6–10]. There are also other mechanisms to produce PBHs through e.g., phase transitions [11], scalar field instabilities [12], the collapse of cos- mic strings [13], etc. PBHs have been studied for decades as they may account for all or part of the dark matter (DM) in the Universe. There is not yet definite proof of the existence of PBHs, but recently, gravitational wave (GW) observation of binary black hole (BBH) mergers is providing rich information on the BH population [14]. Some analysis based on the mass and rate dis- tributions [15–21] or spin properties [22,23] suggests that the observed BBHs could be primordial origin. Another approach to probe PHBs is to search a stochastic GW background (SGWB), which can be formed both at the PBH forma- tion [24–26] and by the superposition of GWs from BBHs [27–31]. The LIGO and Virgo detectors have been improving the upper limit on the amplitude of SGWB [32], and constraints on PBHs through SGWB have been discussed [33–35]. In the future, the upgraded version of the LIGO-Virgo-KAGRA detector network [36] ∗ Corresponding author. E-mail addresses: juan.garciabellido@uam.es (J. García-Bellido), santiago.jaraba@uam.es (S. Jaraba), sachiko.kuroyanagi@csic.es (S. Kuroyanagi). (and later with LIGO-India) and next-generation GW experiments such as Einstein Telescope (ET) [37], Cosmic Explorer (CE) [38], LISA [39], TianQin [40], Taiji [41], DECIGO [42], and so on will allow us to search SGWBs with greater sensitivities for a wide range of frequencies. In this paper, we propose an important additional source of a SGWB, which is formed by overlapped GW bursts from close hyperbolic encounters (CHEs). When considering two interacting BHs, it is possible that BHs will not end up in bound systems depending on the initial condition but instead produce single scattering events. GW bursts from such unbounded interacting systems can be observed by GW experiments and have been studied in the literature [43–50]. In fact, the dense environment at the center of the clusters can enhance the rate of events with an eccentricity near to unity [51], leading to a strong GW burst. Furthermore, if the interaction is strong enough, they can produce interesting dynamics, such as spin induction [52,53] and subsequent mergers [54], etc. If a sufficient number of events occur in the Universe, they overlap and form a SGWB. We make the first estimation of the SGWB amplitude from CHEs and discuss its detectability in future GW experiments, comparing it with the one from BBHs. 2. Stochastic background of GW First, we briefly provide the formulations for calculating the SGWB spectra. The amplitude of a SGWB is commonly charac- terized by Ω GW ≡ (dρ GW /d ln f )/ρ c , where f is the frequency in https://doi.org/10.1016/j.dark.2022.101009 2212-6864/© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by- nc-nd/4.0/).