The effect of the source on the Stochastic Gravitational Wave Background anisotropies

The aim of this master thesis is to analyze the effect of different cosmological sources on the initial anisotropy of the Stochastic Gravitational Wave Background (SGWB). Angular anisotropies in the GW energy density could be an effective tool to distinguish among various sources of GW in the early universe. There are several processes that can generate GWs in the early universe. In this thesis, we focus on inflation, first order phase transitions, and cosmic strings. The primordial density perturbations can be divided into adiabatic perturbations (which are characterized by vanishing entropy perturbation) and isocurvature ones (which have a non-vanishing entropy perturbation). In the case of adiabatic perturbations, GW energy density perturbations behave similarly to Cosmic Microwave Background anisotropies, even if there are some differences due to their non-thermal initial distribution. This is not necessarily the case for isocurvature perturbations. This can have an impact on the angular spectrum of the SGWB and can be a way to distinguish different sources of GW in the early Universe, being at the same time probes of the large-scale gravitational potentials. To study the anisotropies of SGWB we used a Boltzmann approach. We compute analytically the angular power spectrum of the initial condition term for all the cosmological sources of GWs. Then we implement numerically such initial condition term in the Boltzmann code CLASS, adapted for the SGWB.