Mapping the cosmic expansion history from LIGO-Virgo-KAGRA in synergy with DESI and SPHEREx

The measurement of the expansion history of the Universe from the redshift unknown gravitational wave (GW) sources (dark GW sources) detectable from the network of LIGO-Virgo-KAGRA (LVK) detectors depends on the synergy with the galaxy surveys having accurate redshift measurements over a broad redshift range, large sky coverage, and detectability of fainter galaxies.In this work, we explore the possible synergy of the LVK with the spectroscopic galaxy surveys, such as DESI and SPHEREx, to measure the cosmological parameters which are related to the cosmic expansion history and the GW bias parameters. We show that by using the 3D spatial cross-correlation between the dark GW sources and the spectroscopic galaxy samples, we can measure the value of Hubble constant with about 2 per cent and 1.5 per cent precision from LVK-FDESI and LVK-FSPHEREx, respectively within the 5 yr of observation time with 50 per cent duty-cycle. Similarly, the dark energy equation of state can be measured with about 10 per cent and 8 per cent precision from LVK-FDESI and LVK-FSPHEREx, respectively. We find that due to the large sky coverage of SPHEREx than DESI, performance in constraining the cosmological parameters is better from the former than the latter. By combining Euclid along with DESI and SPHEREx, a marginal gain in the measurability of the cosmological parameters is possible from the sources at high redshift (z >= 0.9).

Automated summary

This study explores the synergy between the LVK detectors and spectroscopic galaxy surveys such as DESI and SPHEREx to measure cosmological parameters related to the cosmic expansion history and GW bias parameters. By analyzing the 3D spatial cross-correlation between dark GW sources and spectroscopic galaxy samples, precise measurements of the Hubble constant and dark energy equation of state can be obtained. The combination of Euclid with DESI and SPHEREx shows potential for marginal gains in measuring cosmological parameters, particularly at high redshifts.