Standard Sirens in 2040s: Probing the Cosmic Expansion History with Gravitational Waves and Spectroscopic Galaxy Surveys

Gravitational waves (GWs) from compact binary coalescences have matured into a robust cosmological probe, providing self-calibrated luminosity distance measurements independent of any cosmic distance ladder, hence the term"standard sirens". The binary neutron star merger GW170817 delivered the first such measurement of the Hubble constant, demonstrating that GWs offer a path to precision cosmology with systematics orthogonal to standard cosmological probes. To convert GW distances into cosmological parameters, redshift information is essential. To maximize the scientific potential, the redshift must be obtained from individual galaxies, either by identifying electromagnetic counterparts of GW events (bright sirens) or by statistically associating potential hosts within the GW localization volume (dark sirens). The precision of these redshifts sets the achievable accuracy. Forecasts show that photometric uncertainties degrade cosmological constraints by up to an order of magnitude compared to spectroscopic ones. Wide-field, high-multiplex spectroscopic facilities will therefore be an essential infrastructure for GW cosmology in the 2040s.