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 bΩ̇GW<3.0×10⁻⁹\, Gyr⁻¹ at z~0.06 to bΩ̇GW<2.7×10⁻⁷\, Gyr⁻¹ at z~1.5 (95% C.L.), 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.