Investigating the Cosmological Gravitational Wave Background Anisotropies

A future detection of the Stochastic Gravitational Wave Background (SGWB) with GW experiments is expected to open a new window on early universe cosmology and on the astrophysics of compact objects. Stochastic gravitational waves are the relic gravitational waves from the early evolution of the universe and could be created by the superposition of a large number of independent sources. An eventual detection of such a GW background may possibly provide new and exciting information, that can’t be inferred from CMB measurements. Studying SGWB anisotropies, can offer new tools to discriminate between different sources of GWs. Such anisotropies can be inherited at its production and during its propagation through our perturbed universe. The latter is usually studied through Boltzmann approach, and a subsequent computation of the three-point function (Bispectrum) of the SGWB energy density is also done, which is another method to characterize the cosmological SGWB through its possible deviation from a Gaussian statistics, i.e., non-Gaussianity, which is currently regarded as a fundamental and independent source of information about the physics of the early Universe. The ideal observable to measure the non-Gaussian nature of primordial perturbations, and its eventual scale dependence, is the cosmic microwave background (CMB) radiation. The SGWB, (possibly) generated during inflation, will become a new probe of the primordial non-Gaussianity of the large-scale cosmological perturbations. Another way to do a computation of this kind of SGWB anisotropies is through an approach different from Boltzmann approach. It relies on evolving the propagation of the gravitational waves along perturbed geodesics. It has been first proposed in the 90s for CMB photons, which follow their geodesics after last scattering surface, yet those geodesics will be perturbed again by fluctuations. But this technique tells us only what the final anisotropies are due to propagation effects. The goal of this thesis is then to use the same technique for the Gravitational Wave Background, i.e., follow that different approach to study the SGWB anisotropies.