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

The anisotropies of the Stochastic Gravitational Wave Background (SGWB) produced by merging compact binaries constitute a possible new probe of the Large-Scale Structure (LSS) of the Universe. However, a large shot noise contribution, caused by the discreteness of the GW emitters, is expected to cover the anisotropies induced by the LSS. In this work, we investigate the potential of cross-correlating forthcoming high precision measurements of the SGWB energy density and the Cosmic Microwave Background (CMB) lensing convergence in order to mitigate the effect of shot noise. Combining a detailed modeling of stellar and galactic astrophysics with a novel framework to distribute the GW emitters in the sky, we compute the auto- and cross-correlation power spectra for the two cosmic fields, we evaluate the shot noise contribution and we make a prediction for the signal-to-noise ratio. The results of our analysis show that the SGWB energy density is significantly correlated with the CMB lensing convergence and that the cross-correlation between these two cosmic fields is a powerful tool to reduce the impact of shot noise, paving the way to the detection of the intrinsic SGWB anisotropies.