Titolo della tesi: Cosmic Whispers of the Early Universe: Gravitational Waves and Dark Matter from Primordial Black Holes
Various mechanisms have been suggested for the formation of Primordial Black Holes (PBHs),
and this thesis focuses on the standard mechanism based on the critical collapse of cosmological
fluctuations. The underlying idea is that during inflation, a period of rapid expansion in the early
Universe, large cosmological fluctuations could have been generated. When the cosmic horizon
reached a size comparable to these fluctuations, if the latter were high enough, they could collapse
and form a PBH.
Beyond the fascinating possibility that these compact objects might make up all or part of the
dark matter we observe today, their formation is also associated with the generation of gravitational
waves (GWs). These waves could contribute to the merger events observed by the LIGO/Virgo/KAGRA
Collaboration (LVK) or account for signals detected by pulsar timing array experiments
(PTA). In the first part of this thesis, we investigate the PBH scenario, examining the computation
of the abundance beyond the Gaussian paradigm. In the second part, we discuss how PBH formation
can produce a stochastic GW background and how observations, related to recent experiments
such as LVK and PTA collaborations, can help in distinguishing between different PBH production
models. Finally, in the last part, we investigate some aspects of the interplay between black holes
and fundamental physics in the early Universe, describing some characteristics and challenges of
various PBH production models.