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

TL;DR

This paper investigates how combining gravitational wave data from LIGO-Virgo-KAGRA with galaxy surveys like DESI and SPHEREx can improve measurements of the Universe's expansion history and dark energy properties.

Contribution

It demonstrates the potential of three-dimensional cross-correlation techniques between GW sources and galaxy surveys to precisely determine cosmological parameters.

Findings

Hubble constant can be measured with 1.5-2% precision.

Dark energy equation of state can be constrained within 8-10%.

SPHEREx provides better constraints than DESI due to larger sky coverage.

Abstract

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 \texttt{LIGO-Virgo-KAGRA} (\texttt{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 \texttt{DESI} and \texttt{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 three-dimensional spatial cross-correlation between the dark GW sources and the spectroscopic galaxy samples, we can measure the value of Hubble constant with about $2\%$ and $1.5\%$ precision from \texttt{LVK+DESI} and \texttt{LVK+SPHEREx} respectively within the five years of observation time with $50\%$ duty-cycle. Similarly, the dark energy equation of state can be measured with about $10\%$ and $8\%$ precision from \texttt{LVK+DESI} and \texttt{LVK+SPHEREx} respectively. We find that due to the large sky coverage of \texttt{SPHEREx} than \texttt{DESI}, performance in constraining the cosmological parameters is better from the former than the latter. By combining \texttt{Euclid} along with \texttt{DESI} and \texttt{SPHEREx}, a marginal gain in the measurability of the cosmological parameters is possible from the sources at high redshift ($z\geq 0.9$).