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 Virgo's third observing run (O3) combined with upper limits the earlier O1 O2 runs. Unlike in previous runs advanced detector era, we include Virgo GWB. The are consistent uncorrelated noise, therefore place on strength find that dimensionless energy density $\Omega_{\rm GW}\leq 5.8\times 10^{-9}$ at 95% credible level flat (frequency-independent) GWB, prior which is uniform log 99% sensitivity coming band 20-76.6 Hz; $\leq 3.4 \times 25 Hz power-law GWB spectral index 2/3 (consistent expectations compact binary coalescences), 20-90.6 3.9 10^{-10}$ 3, 20-291.6 Hz. These improve over our by factor 6.0 also arising scalar vector modes, predicted alternative theories gravity; GWBs these polarizations. demonstrate there no evidence correlated noise magnetic origin performing Bayesian analysis allows presence both effective geophysical Schumann resonances. compare to fiducial model merger binaries. Finally, combine observations individual mergers andshow that, design sensitivity, this joint approach may yield stronger constraints rate black holes $z \lesssim 2$ than can be achieved individually resolved alone. [abridged]