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Abstract The inconsistency between experiments in the measurements of the local Universe expansion rate, the Hubble constant, suggests unknown systematics in the existing experiments or new physics. Gravitational-wave standard sirens, a method to independently provide direct measurements of the Hubble constant, have the potential to address this tension. Before that, it is critical to ensure there are no substantial systematics in the standard siren method. A significant systematic has been identified when the viewing angle of the gravitational-wave sources, the compact binary coalescences, was inferred inaccurately from electromagnetic observations of the sources. Such a systematic has led to a more than 10% discrepancy in the standard siren Hubble constant measurements with the observations of binary neutron star merger, GW170817. In this Letter, we develop a new formalism to infer and mitigate this systematic. We demonstrate that the systematic uncertainty of the Hubble constant measurements can be reduced to a level smaller than their statistical uncertainty with 5, 10, and 20 binary neutron star merger observations. We show that our formalism successfully reduces the systematics even if the shape of the biased viewing angle distribution does not follow precisely the model we choose. Our formalism ensures unbiased standard siren Hubble constant measurements when the binary viewing angles are inferred from electromagnetic observations. 

Abstract Advancements in cosmology through next-generation (XG) ground-based gravitational wave (GW) observatories will bring in a paradigm shift. We explore the pivotal role that GW standard sirens will play in inferring cosmological parameters with XG observatories, not only achieving exquisite precision but also opening up unprecedented redshifts. We examine the merits and the systematic biases involved in GW standard sirens utilizing binary black holes, binary neutron stars, and neutron star-black hole mergers. Further, we estimate the precision of bright sirens, golden dark sirens, and spectral sirens for these binary coalescences and compare the abilities of various XG observatories (A ${}^{\mathrm{♯}}$, cosmic explorer, Einstein telescope, and their possible networks). When combining different sirens, we find sub-percent precision over more than 10 billion years of cosmic evolution for the Hubble expansion rateH(z). This work presents a broad view of opportunities to precisely measure the cosmic expansion rate, decipher the elusive dark energy and dark matter, and potentially discover new physics in the uncharted Universe with XG GW detectors.