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tokens: the NSs and BHs form according to the ‘rapid’ and ‘delayed’ SN models of Fryer et al. ( 2012 ) and pulsation pair-instability SN (PPSN) and pair-instability SN (PSN) models of Belczynski et al. ( 2016b ). The NSs and BHs receive natal kicks based on SN fallback on to them, as in Belczynski et al. ( 2008 ). Such fallback slows down the remnants, causing BHs of ≳10 M ⊙ ( Paper I ) to retain in the clusters right after their birth. Furthermore, NSs formed via electron-capture SN (Podsiadlowski et al. 2004 ) also receive small natal kicks and retain in the clusters. In , the PN treatment is handled by the algorithm (Mikkola Tanikawa 1999 ; Mikkola Merritt 2008 ). Such a PN treatment allows for GR evolution of the innermost NS- and/or BH-containing binary of an in-cluster (i.e. gravitationally bound to the cluster) triple or higher order compact subsystem, in tandem with the Newtonian-dynamical evolution of the subsystem (Kozai–Lidov oscillation or chaotic three-body interaction), potentially leading to the binary’s (in-cluster) GR in-spiral and merger. The treatment also undertakes the GR evolution of in-cluster NS/BH-containing binaries that are not a part of a higher order subsystem. As discussed in Paper II (see also the references therein), the moderate density and velocity dispersion in the model clusters make them efficient factories of dynamically assembling PN subsystems, particularly, those comprising BHs. As also discussed in Paper II (see also Anagnostou, Trenti Melatos 2020 ), the vast majority of the GR mergers from these computed model clusters are in-cluster BBH mergers. As also demonstrated therein (see also Banerjee 2020 ), the final in-spiralling phases of such merging BBHs sweep through the LISA and deci-Hertz GW frequency bands before merging in the LVK band. 2.2 Calculation of intrinsic merger rate density from computed model clusters To obtain the intrinsic merger rate density at the present cosmic epoch, ‘mock detection experiments’ are performed in a ‘Model Universe’ that is constructed out of the computed model clusters of Paper II . An ideal GW detector (a detector with zero noise floor) is considered that can detect GW arriving from all GR mergers within a comoving volume whose boundary is at a redshift z max . z max represents an (artificial) horizon, for average source inclination, for a realistic GW detector like LVK. For LVC O1/O2 observing runs, z max ≈ 1 (Abbott et al. 2019b ; Chen et al. 2021 ). However, since an ideal GW detector is considered here, z max will be varied to also address future, ground-based GW detectors of > Hz frequency band (e.g. LIGO A+ upgrade, Einstein Telescope, Cosmic Explorer). If the GR compact-binary merger rate density (per unit comoving volume), , in the Universe has an inherent dependence on the merger event redshift, z event , then the present-day, intrinsic merger rate density, , would depend on the detector horizon, z max (Abadie et al. 2010 ; Abbott et al. 2019b ). Conversely,