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Abstract The detection of GW170817 and the measurement of its redshift from the associated electromagnetic counterpart provided the first gravitational-wave (GW) determination of the Hubble constant (H₀), demonstrating the potential power of standard siren cosmology. In contrast to this “bright siren” approach, the “dark siren” approach can be utilized for GW sources in the absence of an electromagnetic counterpart: One considers all galaxies contained within the localization volume as potential hosts. When statistically averaging over the potential host galaxies, weighting them by physically motivated properties (e.g., tracing star formation or stellar mass) could improve convergence. Using mock galaxy catalogs, we explore the impact of these weightings on the measurement ofH₀. We find that incorrect weighting schemes can lead to significant biases due to two effects: the assumption of an incorrect galaxy redshift distribution, and preferentially weighting incorrect host galaxies during the inference. The magnitudes of these biases are influenced by the number of galaxies along each line of sight, the measurement uncertainty in the GW luminosity distance, and correlations in the parameter space of galaxies. We show that the bias may be overcome from improved localization constraints in future GW detectors, a strategic choice of priors or weighting prescription, and by restricting the analysis to a subset of high-signal-to-noise ratio events. We propose the use of hierarchical inference as a diagnostic of incorrectly weighted prescriptions. Such approaches can simultaneously infer the correct weighting scheme and the values of the cosmological parameters, thereby mitigating the bias in dark siren cosmology due to incorrect host-galaxy weighting. 

ABSTRACT The motion of the centre of mass of a coalescing binary black hole (BBH) in a gravitational potential, imprints a line-of-sight acceleration (LOSA) on to the emitted gravitational-wave (GW) signal. The acceleration could be sufficiently large in dense stellar environments, such as globular clusters (GCs), to be detectable with next-generation space-based detectors. In this work, we use outputs of the cluster monte carlo (cmc) simulations of dense star clusters to forecast the distribution of detectable LOSAs in DECIGO and LISA eras. We study the effect of cluster properties – metallicity, virial and galactocentric radii – on the distribution of detectable accelerations, account for cosmologically motivated distributions of cluster formation times, masses, and metallicities, and also incorporate the delay time between the formation of BBHs and their merger in our analysis. We find that larger metallicities provide a larger fraction of detectable accelerations by virtue of a greater abundance of relatively lighter BBHs, which allow a higher number of GW cycles in the detectable frequency band. Conversely, smaller metallicities result in fewer detections, most of which come from relatively more massive BBHs with fewer cycles but larger LOSAs. We similarly find correlations between the virial radii of the clusters and the fractions of detectable accelerations. Our work, therefore, provides an important science case for space-based GW detectors in the context of probing GC properties via the detection of LOSAs of merging BBHs. 

Abstract The global network of gravitational-wave detectors has completed three observing runs with ∼50 detections of merging compact binaries. A third LIGO detector, with comparable astrophysical reach, is to be built in India (LIGO-Aundha) and expected to be operational during the latter part of this decade. Such additions to the network increase the number of baselines and the network SNR of GW events. These enhancements help improve the sky-localization of those events. Multiple detectors simultaneously in operation will also increase the baseline duty factor, thereby, leading to an improvement in the detection rates and, hence, the completeness of surveys. In this paper, we quantify the improvements due to the expansion of the LIGO global network in the precision with which source properties will be measured. We also present examples of how this expansion will give a boost to tests of fundamental physics.