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Recently, several pulsar timing array (PTA) projects have detected evidence of the existence of a stochastic gravitational wave background (SGWB) in the nanohertz frequency band, providing confidence in detecting individual supermassive black hole binaries (SMBHBs) in the future. Nanohertz GWs emitted by inspiraling SMBHBs encode the luminosity distances of SMBHBs. They can serve as dark sirens to explore the cosmic expansion history via a statistical method to obtain the redshift information of GW sources' host galaxies using galaxy catalogs. The theoretical analysis of the dark siren method relies on the modeling of the population of SMBHBs. Using a population model consistent with the latest SGWB observations is essential, as the SGWB provides significant information about the distribution of SMBHBs. In this work, we employ a quasar-based model, which can self-consistently account for the SGWB amplitude, to estimate the population of SMBHBs. We constrain the Hubble constant using the mock GW data from different detection cases of PTAs in the future. Our results show that a PTA consisting of 100 pulsars with a white noise level of 20 ns could measure the Hubble constant with a precision close to $1\%$ over a 10-year observation period, and a PTA with 200 pulsars may achieve this goal over a 5-year observation period. The results indicate that modeling the SMBHB population significantly influences the analysis of dark sirens, and SMBHB dark sirens have the potential to be developed as a valuable cosmological probe., Comment: 15 pages, 7 figures

Multi-band gravitational-wave (GW) standard siren observations are poised to herald a new era in the study of cosmic evolution. These observations offer higher signal-to-noise ratios and improved localizations compared to those achieved with single-band GW detection, which are crucial for the cosmological applications of dark sirens. In this work, we explore the role multi-band GW synergetic observations will play in measuring cosmological parameters, particularly in comparison with single GW observatory data. We used mock multi-band dark siren data from third-generation GW detectors and the baseline Decihertz Interferometer Gravitational-Wave Observatory to infer cosmological parameters. Our analysis was conservative, involving only the 89 actual GW events from the current Gravitational Wave Transient Catalogs in our data simulation, facilitating a direct comparison with existing dark siren results. Multi-band GW observations significantly improve sky localization accuracy by two to three orders of magnitude over single-band observations, although their impact on luminosity distance error remains limited. This results in a substantial improvement in the constraints on matter density and the Hubble constant, enhancing them by $75\%$ to $85\%$ and $65\%$ to $82\%$, respectively. We conclude that the significant potential of multi-band GW synergistic observations for detecting GW signals and resolving the Hubble tension is highly promising and warrants anticipation., Comment: 11 pages, 4 figures

The 2.5-generation (2.5G) ground-based gravitational wave (GW) detectors LIGO Voyager and NEMO are expected to be operational in the late 2020s and early 2030s. In this work, we explore the potential of GW standard sirens observed by the 2.5G GW detectors in measuring cosmological parameters, especially for the Hubble constant. Using GWs to measure cosmological parameters is inherently challenging, especially for 2.5G detectors, given their limited capability, which results in weaker constraints on cosmological parameters from the detected standard sirens. However, the measurement of the Hubble constant using standard siren observations from Voyager and NEMO is still promising. For example, using bright sirens from Voyager and NEMO can measure the Hubble constant with a precision of about $2\%$ and $6\%$ respectively, and using the Voyager-NEMO network can improve the precision to about $1.6\%$. Moreover, bright sirens can be used to break the degeneracy of cosmological parameters generated by CMB data, and to a certain extent, 2.5G detectors can also play a role in this aspect. Observations of dark sirens by 2.5G detectors can achieve relatively good results in measuring the Hubble constant, with a precision of within $2\%$, and if combining observations of bright and dark sirens, the precision of the Hubble constant measurement can reach about $1.4\%$. Finally, we also discussed the impact of the uncertainty in the binary neutron star merger rate on the estimation of cosmological parameters. We conclude that the magnificent prospect for solving the Hubble tension is worth expecting in the era of the 2.5G ground-based GW detectors., Comment: 28 pages, 13 figures

In the coming decades, the space-based gravitational-wave (GW) detectors such as Taiji, TianQin, and LISA are expected to form a network capable of detecting millihertz GWs emitted by the mergers of massive black hole binaries (MBHBs). In this work, we investigate the potential of GW standard sirens from the Taiji-TianQin-LISA network in constraining cosmological parameters. For the optimistic scenario in which electromagnetic (EM) counterparts can be detected, we predict the number of detectable bright sirens based on three different MBHB population models, i.e., pop III, Q3d, and Q3nod. Our results show that the Taiji-TianQin-LISA network alone could achieve a constraint precision of $0.9\%$ for the Hubble constant, meeting the standard of precision cosmology. Moreover, the Taiji-TianQin-LISA network could effectively break the cosmological parameter degeneracies generated by the CMB data, particularly in the dynamical dark energy models. When combined with the CMB data, the joint CMB+Taiji-TianQin-LISA data offer $\sigma(w)=0.036$ in the $w$CDM model, which is close to the latest constraint result obtained from the CMB+SN data. We also consider a conservative scenario in which EM counterparts are not available. Due to the precise sky localizations of MBHBs by the Taiji-TianQin-LISA network, the constraint precision of the Hubble constant is expected to reach $1.2\%$. In conclusion, the GW standard sirens from the Taiji-TianQin-LISA network will play a critical role in helping solve the Hubble tension and shedding light on the nature of dark energy., Comment: 22 pages, 10 figures; published in Science China Physics Mechanics & Astronomy

Gravitational waves (GWs) from compact binary coalescences encode the absolute luminosity distances of GW sources. Once the redshifts of GW sources are known, one can use the distance-redshift relation to constrain cosmological parameters. One way to obtain the redshifts is to localize GW sources by GW observations and then use galaxy catalogs to determine redshifts from a statistical analysis of redshift information of the potential host galaxies, commonly referred to as the dark siren method. The third-generation (3G) GW detectors are planned to work in the 2030s and will observe numerous compact binary coalescences. Using these GW events as dark sirens requires high-quality galaxy catalogs from future sky survey projects. The China Space Station Telescope (CSST) will be launched in 2024 and will observe billions of galaxies within a 17500 deg$^2$ survey area with redshift up to $z\sim 4$, providing photometric and spectroscopic galaxy catalogs. In this work, we simulate the CSST galaxy catalogs and the 5-year GW data from the 3G GW detectors and combine them to infer the Hubble constant ($H_0$). Our results show that the measurement precision of $H_0$ could reach the sub-percent level, meeting the standard of precision cosmology. We conclude that the synergy between CSST and the 3G GW detectors is of great significance in measuring the Hubble constant., Comment: 13 pages, 5 figures; accepted for publication in Science China Physics, Mechanics & Astronomy