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- Post-inflationary effects in primordial black hole formation and scalar-induced gravitational wavesPublication . del Corral Martínez, Daniel; Marto, João Pedro de Jesus; Kumar, Korumilli Sravan; Olmedo Nieto, Javier AntonioThis thesis explores new aspects of primordial black hole (PBH) formation from scalar perturbation instabilities in the early Universe and the associated production of induced gravitational waves (GWs). The key contributions of this thesis are: • The inclusion of significant effects from small-scale perturbations that remain subhorizon during inflation, which are often neglected in the literature. • An alternative estimation to the standard Press–Schechter formalism for the PBH abundance is provided by the Khlopov–Polnarev formalism. This approach is particularly well-suited for inflaton matter-dominated era and accounts for critical effects such as pressure suppression and the influence of non-sphericity in the dynamics of perturbations. The central focus is on the nearly matter-dominated post-inflationary preheating phase, where the inflaton oscillates at the minimum of its potential prior to its decay into ultralight particles (reheating phase). These oscillations drive parametric instabilities in the scalar perturbations via the Mukhanov-Sasaki equation. Particularly, at small scales and with large deviations of the inflaton potential from a quadratic shape, these perturbations strongly amplify, potentially leading to PBH formation. To further characterize how these perturbations collapse into PBHs, we apply three complementary criteria: (1) the modes must lie within some specific range of scales (instability band) to be affected by the instabilities, (2) the physical size of the modes must be larger than the Jeans length and (3) a critical threshold based on the minimum time for collapse of these perturbations. Each of these criteria improves the estimation of the PBHs mass fraction. The induced GWs, influenced by these small-scale instabilities through second-order scalartensor coupling, exhibit rapid and significant energy density amplification at high frequencies. Additionally, we explore the implications of an epoch of PBHs overproduction and the temporary domination of the energy density of the universe. This PBH-dominated phase also leaves a distinctive imprint on the GW spectrum, providing a powerful probe of PBH scenarios with current and future GW detectors. These results enhance our understanding of early Universe physics and establish new avenues for testing inflationary models through PBH formation and gravitational wave signals.