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The anisotropies of the Stochastic Gravitational-Wave Background (SGWB)produced by merging compact binaries constitute a possible new probe of theLarge-Scale Structure (LSS). However, the significant shot noise contributioncaused by the discreteness of the GW sources and the poor angular resolution ofthe instruments hamper the detection of the intrinsic anisotropies induced bythe LSS. In this work, we investigate the potential of cross-correlatingforthcoming high precision measurements of the SGWB energy density and theCosmic Microwave Background (CMB) lensing convergence to mitigate the effect ofshot noise. Combining a detailed model of stellar and galactic astrophysicswith a novel framework to distribute the GW emitters in the sky, we compute theauto- and cross-correlation power spectra for the two cosmic fields, evaluatethe shot noise contribution and predict the signal-to-noise ratio. The resultsof our analysis show that the SGWB energy density correlates significantly withthe CMB lensing convergence and that the cross-correlation between these twocosmic fields reduces the impact of instrumental and shot noise. Unfortunately,the S/N is not high enough to detect the intrinsic SGWB anisotropies.Nevertheless, a network composed of both present and future generation GWinterferometers, operating for at least 10 yrs, should be able to measure theshot noise contribution.

Detectability of the cross-correlation between CMB lensing and stochastic GW background from compact object mergers