Cosmological Stochastic Backgrounds of Gravitational Waves

In the following, we first present some generalities on GW signals from the early universe, and then focus on two processes that can generate a stochastic GW background: after having briefly overviewed standard slow roll inflation, we thoroughly discuss the main topic of this dissertation, first order phase transitions (PTs) in the early universe. The manuscript is organised as follows. In chapter 2 we provide a definition of GWs, initially on a flat space-time, and then focusing on the relevant case of a Friedmann-Lemaitre-Robertson-Walker (FLRW) background, together with some noteworthy solutions of the GW equation of motion. In chapter 3, after discussing why any GW background produced in the early universe is of stochastic nature, we present a general characterization of a statistically homogeneous and isotropic stochastic gravitational wave background (SGWB). In chapter 4 we review the present constraints on SGWBs, and discuss some of the characteristics of current and future GW detectors. In chapter 5 we discuss the irreducible SGWB arising from quantum vacuum fluctuations in standard inflation, and its evolution until today. Finally, chapter 6 is dedicated to first order phase transitions beyond the standard model of particle physics, both related and unrelated to the electroweak symmetry breaking. (author)