Astrophysical background of gravitational waves: anisotropies, polarization and cross-correlations with cosmological observables

The astrophysical background of gravitational waves (AGWB) is composed by the incoherent superposition of gravitational wave signals emitted by a large number of resolved and unresolved astrophysical sources from the onset of stellar activity until today. I present a theoretical framework to fully characterize the AGWB in terms of energy density anisotropies and polarization and I present the first numerical predictions for the angular power spectra of anisotropies in the LIGO/Virgo and LISA frequency bands, and for cross-correlations with electromagnetic observables e.g. weak lensing and galaxy number counts. I show that the anisotropies of the stochastic background contain additional information on sub-galactic processes, complementary to the isotropic background and individual mergers. I then illustrate and discuss the astrophysical implications of this study and I present my ongoing work on noise characterization.