Upper limits on the isotropic gravitational-wave background from Advanced LIGO and Advanced Virgo's third observing run

We report results of a search for an isotropic gravitational-wave background (GWB) using data from Advanced LIGO's and Advanced Virgo's third observing run (O3) combined with upper limits from the earlier O1 and O2 runs. Unlike in previous observing runs in the advanced detector era, we include Virgo in the search for the GWB. The results are consistent with uncorrelated noise, and therefore we place upper limits on the strength of the GWB. We find that the dimensionless energy density $\Omega_{\rm GW}\leq 5.8\times 10^{-9}$ at the 95% credible level for a flat (frequency-independent) GWB, using a prior which is uniform in the log of the strength of the GWB, with 99% of the sensitivity comi…