Non-linear effects on the Cosmological Gravitational Wave Background anisotropies

The Cosmological Gravitational Wave Background (CGWB) anisotropies contain valuable information about the physics of the early universe. Given that General Relativity is intrinsically non-linear, it is important to look beyond first-order contributions in cosmological perturbations. In this work, we present a non-perturbative approach for the computation of the CGWB anisotropies at large scales, providing the extension of the initial conditions and the Sachs-Wolfe effect for the CGWB, which encodes the full non-linearity of the scalar metric perturbations. We also derive the non-perturbative expression for three-point correlation of the gravitational wave energy density perturbation in the case of an inflationary CGWB with a scale-invariant power spectrum and negligible primordial non-Gaussianity. We show that, under such conditions, the gravitational wave energy density perturbations are lognormally distributed, leading to an interesting effect such as intermittency.