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Cosmological gravitational-wave backgrounds are an exciting science target for next-generation ground-based detectors, as they encode invaluable information about the primordial Universe. However, any such background is expected to be obscured by the astrophysical foreground from compact-binary coalescences. We propose a novel framework to detect a cosmological gravitational-wave background in the presence of binary black holes and binary neutron star signals with next-generation ground-based detectors, including Cosmic Explorer and the Einstein Telescope. Our procedure involves first removing all the individually resolved binary black hole signals by notching them out in the time-frequency domain. Then, we perform joint Bayesian inference on the individually resolved binary neutron star signals, the unresolved binary neutron star foreground, and the cosmological background. For a flat cosmological background, we find that we can claim detection at 5σ level when Ωₑ₄₅≥2. 7×10^-12/sqrtT₎₁ₒ/yr, where T₎₁ₒ is the observation time (in years), which is within a factor of ≲2 from the sensitivity reached in the absence of these astrophysical foregrounds.
Zhong et al. (2025) studied this question.