Primordial Black Holes: from Theory to Gravitational Wave Observations

Primordial Black Holes (PBH) can form in the early universe and might comprise a significant fraction of the dark matter. Interestingly, they are accompanied by the generation of Gravitational Wave (GW) signals and they could contribute to the merger events currently observed by the LIGO/Virgo Collaboration (LVC). In this thesis, we study the PBH scenario, addressing various properties at the formation epoch and the computation of abundance beyond the Gaussian paradigm, while also developing the theoretical description of PBH evolution through accretion and mergers, with particular focus on modelling their GW signatures. In a second part, we compare the primordial scenario with current GW data, seizing the possible contribution of PBH binaries to LVC signals and forecasting the potential of future GW detectors, such as Einstein Telescope and LISA, to detect mergers of primordial binaries and the stochastic GW background induced at second order by the PBH formation mechanism.