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With about a hundred binary black hole (BBH) mergers detected byLIGO-Virgo-KAGRA, and with several hundreds expected in the current O4 run, GWsare revolutionizing our understanding of the universe. Some BBH sources are toofaint to be individually detected, but collectively they may give rise to astochastic GW background (SGWB). In this paper, we calculate the SGWBassociated with BBH mergers dynamically assembled in dense star clusters, usingstate-of-the-art numerical models. We discuss the role of modeling theevolution of the mass distribution of BBH mergers, which has significantimplications for model selection and parameter estimation, and could be used todistinguish between different channels of BBH formation. We demonstrate how thebirth properties of star clusters affect the amplitude and frequency spectrumof the SGWB, and show that upcoming observation runs of ground-based GWdetectors may be sensitive enough to detect it. Even in the case of anon-detection, we find that GW data can be used to constrain the highlyuncertain cluster birth properties, which can complement direct observations ofyoung massive clusters and proto-star clusters in the early universe by JWST.

On the Stochastic Gravitational Wave Background from Binary Black Hole Mergers Dynamically Assembled in Dense Star Clusters