The astrophysical background of gravitational waves (AGWB) is made up 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 which is based on the resolution of Olbers' paradox. I also discuss how these results can be recovered from a Boltzmann approach with an ad-hoc GW emissivity. It is found that the predictions of the signal angular statistics depend on the astrophysical modelling, hence this observable opens a new window on the history of compact objects populations.

IAP – Institut d’Astrophysique de Paris