The Stochastic Gravitational-Wave Background (SGWB) is expected to be a key observable for Gravitational-Wave (GW) interferometry. Its detection will open a new window on early Universe cosmology, on the astrophysics of compact objects and, as shown in this Letter, on the particle physics content of the Universe. In this Letter we show that, besides their effects on the Cosmic Microwave Background (CMB) and on Large Scale Structure (LSS), relativistic particles in the early Universe leave a clear imprint on the anisotropies of the SGWB. In particular we show that a change in the number of decoupled relativistic particles shifts the angular power spectrum of the SGWB, as both the Sachs-Wolfe (SW) and the Integrated Sachs-Wolfe (ISW) terms are affected. Being very large-angle effects, these lead to new testable predictions for future GW interferometers.

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One of the main pillars of the ΛCDM model is the Cosmological Principle, which states that our Universe is statistically isotropic and homogeneous on large scales. Here we test this hypothesis using the Astrophysical Gravitational Wave Background (AGWB) expected to be measured by the Einstein Telescope-Cosmic Explorer network; in particular we perform a numerical computation of the AGWB dipole, evaluating the intrinsic contribution due to clustering and the kinematic effect induced by the observer motion. We apply a component separation technique in the GW context to disentangle the kinematic dipole, the intrinsic dipole and the shot noise (SN), based on the observation of the AGWB at different frequencies. We show how this technique can also be implemented in matched-filtering to minimize the covariance which accounts for both instrumental noise and SN. Since GW detectors are essentially full-sky, we expect that this powerful tool can help in testing the isotropy of our Universe in the next future.

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