Three-band dark-siren cosmology with intermediate-mass black hole binaries: synergy of Taiji, LGWA, and Einstein Telescope

Abstract

Gravitational-wave (GW) dark sirens provide an independent probe of the cosmic expansion history. Their cosmological constraining power, however, depends critically on precise luminosity-distance measurements and sky localizations for cross-matching with galaxy catalogs. Multiband GW observations can track GW events across different frequency bands and thus improve both. Motivated by this, we forecast the cosmological potential of intermediate-mass black hole binaries (IMBHBs) observed by a three-band GW detector network composed of Taiji (TJ), the Lunar Gravitational-wave Antenna (LGWA), and the Einstein Telescope (ET). We simulate detectable IMBHB populations and analyze them with a hierarchical Bayesian dark-siren framework that includes galaxy-catalog completeness and redshift uncertainties. We find that the TJ-LGWA-ET network outperforms all two-detector configurations considered here. In the $Λ$CDM model, it constrains the Hubble constant and matter density to $\sim 0.12\%$ and $\sim 0.6\%$, respectively. In the $w$CDM model, a 4-year dark-siren sample alone constrains the dark-energy equation-of-state parameter $w$ to $\sim 2.7\%$. Adding baryon acoustic oscillation (BAO) and Type Ia supernova (SNe Ia) data improves the $w$ constraint to $\sim 2.1\%$, slightly better than that from the current CMB+BAO+SNe Ia combination. We also show that the final constraints remain sensitive to IMBHB population assumptions and galaxy-catalog limitations, which highlights the need for deep galaxy surveys with precise redshift measurements.

Figures (7)

• Figure 1: Comparison between multi-band GW detector sensitivities and the frequency-domain detectability of IMBHBs. The horizontal axis shows the frequency and the vertical axis shows the characteristic strain, both on logarithmic scales. The colored solid lines display the noise characteristic-strain curves of three detectors: TJ (green), LGWA (pink), and ET (blue). The four black curves with different line styles represent the signal tracks of equal-mass IMBHBs ($10^2\!+\!10^2$, $10^3\!+\!10^3$, $10^4\!+\!10^4$, and $10^5\!+\!10^5\,M_\odot$) at $z=1$, simulated using the IMRPhenomD waveform and converted to characteristic strain via $h_c = 2f|\tilde{h}_+|$. Open circles along each black track mark the approximate beginnings of the merger phase. The blue, green, orange, and red filled markers indicate the signal locations at $4$ years, $1$ year, $30$ days, and $1$ day before the merger.
• Figure 2: Redshift distributions of detectable events for different detector networks under the detection threshold of $\mathrm{SNR}\ge 8$ during 1-year observation. The colored step histograms show the network-selected samples for LGWA+ET, LGWA+TJ, ET+TJ, and LGWA+ET+TJ, where the solid lines correspond to the $z2$ population model and the dotted lines correspond to the $z5$ population model; colors distinguish detector networks. The gray solid and gray dotted curves denote the total IMBHB distributions for the $z2$ and $z5$ models, respectively.
• Figure 3: Cumulative distribution functions (CDFs) of the relative luminosity distance error $\sigma_{d_{\rm L}}/d_{\rm L}$ and the 90% sky localization error $\Delta \Omega_{90\%}$ for different detector networks. The top panel shows the CDF of the fractional luminosity-distance uncertainty, where the y-axis value at a given x-axis value $X$ in the CDF curve represents the proportion of GW events with $\sigma_{d_{\rm L}}/d_{\rm L}$ less than $X$ relative to the total number of events. The bottom panel shows the CDF of the 90% credible sky-localization area, $\Delta\Omega_{90\%}$ deg$^2$, following analogously.
• Figure 4: Schematic flowchart of the dark-siren analysis. The mock GW sample provides the distance and sky-localization information, which are combined with the mock galaxy catalog and the selection function to construct the event likelihood and to obtain the joint posterior for the cosmological parameters.
• Figure 5: Constraint precisions of $H_0$ and $\Omega_{\rm m}$ for different detector network configurations. For each network configuration, the blue bar (referencing the left y-axis) and the red bar (referencing the right y-axis) represent the relative uncertainties $\sigma_{H_0}/H_0$ and $\sigma_{\Omega_{m}}/\Omega_{m}$ in percentage, respectively.