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In recent years, constraints on the Hubble parameter using multiple dark sirens have been made,relying on a galaxy catalogue, correlations between the mass and redshift distributions, or both. Those studies have typically used only significant gravitational wave candidates. In this work, we present a framework for cosmological inference that bypasses per-candidate parameter estimation, uses only detection-level information. This allows the population inference from a candidate list produced directly by a search pipeline, without additional selection cuts. Our method is particularly suited to extracting information from marginal candidates, which are essential for probing the distant universe.

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