Tomographic constraints on the production rate of gravitational waves from astrophysical sources

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 less than or similar to 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 < b(Omega)over dot(GW)> <3.0 x 10(-9) Gyr(-1) at z similar to 0.06 to < b(Omega)over dot(GW)> <2.7 x 10(-7) Gyr(-1) at z similar to 1.5 (95% confidence level), assuming a frequency spectrum of the form f(2/3) (corresponding to an astrophysical background of binary mergers), and a reference frequency f(ref) = 25 Hz. Although these constraints are similar to 2 orders of magnitude higher than the expected signal, we show that a detection may be possible with future experiments.