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≲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 bω˙GW<3.0×10-9 Gyr-1 at z∼0.06 to bω˙GW<2.7×10-7 Gyr-1 at z∼1.5 (95% confidence level), assuming a frequency spectrum of the form f2/3 (corresponding to an astrophysical background of binary mergers), and a reference frequency fref=25 Hz. Although these constraints are ∼2 orders of magnitude higher than the expected signal, we show that a detection may be possible with future experiments.