Gravitational Wave Background Anisotropies: Probing Early and Late Universe Cosmology with Interferometers

In this Thesis, we have characterized the anisotropies of stochastic backgrounds of cosmological (CGWB) and astrophysical (AGWB) origin. We have considered as sources of cosmological gravitational waves the quantum fluctuations of the metric during inflation, primordial black holes and phase transitions, while for the astrophysical background we have computed the signal generated by the superposition of gravitational waves emitted by binary black holes. The anisotropies of the CGWB have been computed by introducing a distribution function for the primordial gravitons and solving the Boltzmann equation in the perturbed Universe. In this Thesis we have computed the initial conditions on the distribution function of gravitons, finding large non-adiabatic contributions in the inflationary case. Furthermore, we have computed numerically the angular power spectrum of the CGWB and of the cross-correlation of the Cosmic Microwave Background (CMB) and the CGWB. By exploiting the large correlation between the CMB and the CGWB, we forecasted the detectability of cosmological parameters with future interferometers like Einstein Telescope (ET) and Cosmic Explorer (CE). On the other hand, the anisotropies of the AGWB have been computed by using the Cosmic Rulers formalism, distinguishing between the intrinsic (due to overdensity in the number of sources), the kinetic (due to our peculiar motion with respect to the sources) and the shot noise (due to Poisson fluctuations in the number of sources) contributions. In particular, we have found that the shot noise fluctuations generate a net amount of circular polarization which is detectable by 3g detectors. Furthermore, thanks to the typical frequency dependence of the anisotropies, we have found that our peculiar motion can be estimated by future detectors like ET and CE with high precision, thanks to a faithful reconstruction of the map of the kinetic dipole.