Cosmological Gravitational Wave Background as a window into the early Universe

This thesis is devoted to the study of the Cosmological Gravitational Wave Background (CGWB) anisotropies, as well as to a new mechanism of gravitational waves production in the early Universe. In the first part of the thesis, we focus on the initial conditions for anisotropies of the CGWB generated by quantum fluctuations of the metric during inflation. The non-thermal nature of the CGGW makes it non-trivial to define the initial conditions for the local density field of the graviton distribution, which determines the initial contribution to CGWB anisotropies. The adiabatic initial condition is violated due to presence of independent tensor perturbations during inflation. We obtain these non-adiabatic initial conditions by explicitly computing the energy-momentum tensor of GWs. This leads to an enhancement of the total CGWB angular power spectrum compared to the adiabatic case. Then, we explore the non-linear effects on the CGWB anisotropies. We present a non-perturbative approach for the computation of CGWB anisotropies at large scales and the 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. Under such conditions, the energy density perturbation of gravitational waves is lognormally distributed leading to an interesting effect, known as spatial intermittency. In the last part of the thesis, we introduce a novel mechanism that can generate gravitational waves from vacuum fluctuations after inflation. The CGWB is induced by the scalar perturbations of the metric during the radiation-dominated epoch via the cosmological gravitational particle production mechanism. We find that the resulting GW spectrum peaks around the GHz frequency range, which distinguishes it from other astrophysical and cosmological sources.