Synergy between CSST and third-generation gravitational-wave detectors: Inferring cosmological parameters using cross-correlation of dark sirens and galaxies

TL;DR

This work demonstrates that cross-correlating CSST photometric galaxies with dark sirens detected by 3G gravitational-wave detectors enables precise cosmological inferences through distance–redshift mapping. Using an angular power-spectrum framework with Limber approximation and Fisher-matrix forecasting, the authors show that combining galaxy auto-, GW auto-, and galaxy–GW cross-correlations yields $H_0$ at the ~1% level and meaningful constraints on $ S$, $A_s$, and GW clustering bias, particularly for a 10-year ET2CE network. The CSST galaxy sample’s deep redshift reach and large sky coverage, paired with improved GW localization and distance precision from networks like ET2CE, breaks degeneracies and enhances constraints beyond what galaxy or GW data could achieve alone. This cross-correlation methodology offers a complementary approach to dark siren cosmology that is less dependent on complete galaxy catalogs and population models, and it provides insights into GW source formation channels through the constrained GW clustering bias parameters.

Abstract

Gravitational-wave (GW) events are generally believed to originate in galaxies and can thus serve, like galaxies, as tracers of the universe's large-scale structure. In GW observations, waveform analysis provides direct measurements of luminosity distances; however, the redshifts of GW sources cannot be determined due to the mass-redshift degeneracy. By cross-correlating GW events with galaxies, one can establish a correspondence between luminosity distance and redshift shells, enabling cosmological inference. In this work, we explore the scientific potential of cross-correlating GW sources detected by third-generation (3G) ground-based GW detectors with the photometric redshift survey of the China Space Station Survey Telescope (CSST). We find that the constraint precisions of the Hubble constant and the matter density parameter can reach $1.04\%$ and $2.04\%$, respectively. The GW clustering bias parameters $A_{\rm GW}$ and $γ$ can be constrained to $1.52\%$ and $4.67\%$, respectively. These results highlight the significant potential of the synergy between CSST and 3G ground-based GW detectors in constraining cosmological models and probing GW source formation channels using cross-correlation of dark sirens and galaxies.

Figures (7)

• Figure 1: Angular power spectra and noise contributions. The upper panel shows the dependence on multipoles $\ell$ in the redshift bin $z\in[0.65,0.73]$, while the lower panel presents the redshift evolution at $\ell=30$. Green, yellow, and blue solid curves correspond to the galaxy auto-spectrum, GW auto-spectrum, and galaxy-GW cross-spectrum, respectively. Black and red dashed lines indicate the noise in the galaxy and GW auto-spectra, respectively.
• Figure 2: SNRs for the auto-correlation of the CSST photometric galaxy sample (left), the auto-correlation of GW source catalogs from the ET2CE detector network (center), and their cross-correlation (right). Each small square represents the analysis result for a specific combination of redshift and luminosity-distance bins, with the color indicating the SNR value within that bin.
• Figure 3: Number density distributions as a function of redshift. The left panel shows galaxies from the CSST survey, while the right panel presents GW events from 1 year by the ET2CE network. The dashed curves denote the original number distributions, and the solid curves indicate the effective number distributions after applying the window function as given in eq. \ref{['eq:9']}. Grey vertical lines mark the bin edges.
• Figure 4: Cumulative distribution functions of the relative luminosity distance error $\Delta d_{\mathrm {L}}/d_{\mathrm {L}}$ and the 90% sky localization error $\Delta \Omega_{90\%}$ for three GW detector configurations. The left panel presents $\Delta d_{\mathrm {L}}/d_{\mathrm {L}}$, where the y-axis value at a given x-axis value $X$ in the CDF curve represents the proportion of GW events with $\Delta d_{\mathrm {L}}/d_{\mathrm {L}}$ less than $X$ relative to the total number of events. The interpretation of the CDF curve for $\Delta \Omega_{90\%}$ in the right panel follows analogously.
• Figure 5: Constraints on cosmological and GW clustering bias parameters derived from the individual analyses of the galaxy auto-correlation, the galaxy-GW cross-correlation, and the joint analysis of both alongside the GW auto-correlation, respectively, using the 10-year GW sample of ET2CE and the CSST photometric galaxy sample.