Generating primordial black holes in non-canonical inflation

Among the candidates for dark matter, Primordial Black Holes are extremely promising, as they do not require the introduction of new physics beyond the Standard Model of particle physics. These objects can arise from the collapse of overdense regions generated by the curvature perturbation generated during inflation. The probability distribution of these overdense regions is related to the power spectrum of the scalar perturbation which must be enhanced by compared to the perturbation at CMB scale in order for the collapse to generate enough Primordial Black Holes to account for the dark mater budget we observe today. In this thesis we discuss two possible amplification mechanism in non-canonical inflation, employing a decreasing sound speed. In the first case we consider a model which starts in a slow-roll regime at CMB scale. Later during inflation the field enters in a non-canonical regime and it approaches the k-inflation attractor. During this kinetically driven transient phase the sound speed and the slow roll parameter $\epsilon$ decrease exponentially and the power spectrum of the curvature perturbation gets amplified. We then consider a DBI model where we consider the presence of a gaussian spike in the warp factor, thus leading to the transition, from the canonical phase at CMB scales to a strongly non-canonical regime. In this latter phase, the sound speed of perturbation is much smaller than 1, and leads to an amplification of the scalar perturbation power spectrum.