  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 ($z\geq
0.9$).
