  Using an optimal quadratic estimator, we measure the large-scale
cross-correlation between maps of the stochastic gravitational-wave intensity,
constructed from the first three LIGO-Virgo observing runs, and a suite of
tomographic samples of galaxies covering the redshift range $z\lesssim 2$. We
do not detect any statistically significant cross-correlation, but the
tomographic nature of the data allows us to place constraints on the
(bias-weighted) production rate density of gravitational waves by astrophysical
sources as a function of cosmic time. Our constraints range from $\langle
b\dot{\Omega}_{\rm GW}\rangle<3.0\times10^{-9}\,{\rm Gyr}^{-1}$ at $z\sim0.06$
to $\langle b\dot{\Omega}_{\rm GW}\rangle<2.7\times10^{-7}\,{\rm Gyr}^{-1}$ at
$z\sim1.5$ (95\% C.L.), assuming a frequency spectrum of the form $f^{2/3}$
(corresponding to an astrophysical background of binary mergers), and a
reference frequency $f_{\rm ref}=25\,{\rm Hz}$. Although these constraints are
$\sim2$ orders of magnitude higher than the expected signal, we show that a
detection may be possible with future experiments.
