Inferring cosmological parameters from galaxy and dark sirens cross-correlation

TL;DR

The paper introduces a robust, tomographic cross-correlation framework between GW dark sirens and galaxy tracers to infer cosmology without relying on complete galaxy-host catalogs. By modeling galaxies and GWs as biased tracers and computing a full likelihood over angular power spectra $C_\ell$, it forecasts cosmological constraints for current 2G networks (HLVK, HLVIK) and future 3G detectors (ET2CE), cross-correlated with Euclid-like surveys. The results show that 3G detectors could measure the Hubble constant $H_0$ to about $1\%$ (indeed $\sim0.7\%$ when combining information) and that GW-galaxy cross-correlation is highly complementary to galaxy auto-correlation, significantly improving constraints on other parameters and helping to address the Hubble tension. The method remains robust to galaxy catalog incompleteness and highlights the value of joint GW and galaxy analyses for precision cosmology, with potential extensions to curved spacetimes.

Abstract

The number of observed gravitational wave (GW) events is growing fast thanks to rapidly improving detector sensitivities. GWs from compact binary coalescences like Black Holes or Neutron Stars behave like standard sirens and can be used as cosmological probes. To this aim, generally, the observation of an electromagnetic counterpart and the measurement of the redshift are needed. However, even when those are not available, it is still possible to exploit these "dark sirens" via statistical methods. In this work, we explore a method that exploits the information contained in the cross-correlation of samples of GW events with matter over-density tracers like galaxy catalogues. Contrary to other currently employed dark-sirens methods, this approach does not suffer from systematic errors related to the incompleteness of the galaxy catalogue. To further enhance the technique, we implement tomography in redshift space for the galaxy catalogue and luminosity distance space for the GWs. We simulate future data collected by the array of currently existing detectors, namely LIGO, Virgo, and Kagra, as well as planned third-generation ones such as the Einstein Telescope and Cosmic Explorers. We cross-correlate these data with those from upcoming photometric galaxy surveys such as Euclid. We perform a sensitivity forecast employing a full-likelihood approach and explore the parameter space with Monte Carlo Markov Chains. We find that with this method, third-generation detectors will be able to determine the Hubble constant $H_0$ with an error of only 0.7%, which is enough to provide decisive information to shed light on the Hubble tension. Furthermore, for the other cosmological parameters, we find that the GWs and galaxy surveys information are highly complementary, and the use of both significantly improves the ability to constrain the underlying cosmology.

Figures (12)

• Figure 1: For the galaxy redshift survey assumed in our forecast, normalised density distribution $dn^{G_i}/dz$ as a function of $z$ for each of our 10 $z$-bins. The upper $x$-axis shows the corresponding luminosity distance $D_L$ according to the fiducial cosmology.
• Figure 2: Left: Distribution of detectable BBH over distance for the 3 detector configuration considered. The upper $x$-axis shows the equivalent $z$ computed with the fiducial cosmology. Right: the same, but for BNS.
• Figure 3: Left: Luminosity distance relative errors as a function of redshift employed in the analysis. Right: Angular resolutions as a function of redshift employed in the analysis, as taken from Calore:2020bpd.
• Figure 4: Left: normalised density distribution $dn^{W_i}/dD_L$ as a function of $D_L$ for each of our 5 $D_L$-bins for the HLVIK BBH case. The upper $x$-axis shows redshifts converted from $D_L$ using the fiducial cosmology. Right: same for the ET2CE BBH case.
• Figure 5: Cross-correlation SNR contributions as function of $\ell$ (see \ref{['eq:SNR2']}) for the various GW source and detector configurations considered in the analysis for 10 years of observation. The solid line shows the actual SNR, while the dotted line shows the results assuming perfect localisation, i.e, no beam effect, $\sigma^W_i=0$ for all bins in \ref{['eq:beam_ang']}. The total SNR is reported in \ref{['tab:SNR']}.