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General Relativity provides us with an extremely powerful tool to extract atthe same time astrophysical and cosmological information from the StochasticGravitational Wave Backgrounds (SGWBs): the cross-correlation with othercosmological tracers, since their anisotropies share a common origin and thesame perturbed geodesics. In this letter we explore the cross-correlation ofthe cosmological and astrophysical SGWBs with Cosmic Microwave Background (CMB)anisotropies, showing that future GW detectors, such as LISA or BBO, have theability to measure such cross-correlation signals. We also present, as a newtool in this context, constrained realization maps of the SGWBs extracted fromthe high-resolution CMB {\it Planck} maps. This technique allows, in thelow-noise regime, to faithfully reconstruct the expected SGWB map by startingfrom CMB measurements.

Cross-correlating Astrophysical and Cosmological Gravitational Wave Backgrounds with the Cosmic Microwave Background