Explicit inflationary models for the enhancement of primordial fluctuations

The nature of dark matter remains one of the fundamental quests of modern physics. One of its simplest explanations is based on the assumption that a large amount of DM is made of black holes of primordial origin (PBHs). Such an explanation is compelling since it does not rely on the existence of new particles or some modification of the gravitational interaction. PBHs can form from the collapse of large density perturbations in the early universe, that could have formed from the inflaton fluctuations. An amplification of these fluctuations of several orders of magnitude with respect to those probed by Cosmic Microwave Background (CMB) radiation is necessary to trigger the collapse. In this work, two different scenarios of amplification are studied. First, we analyze the case of a minimally coupled inflaton. The reconstruction of a class of potentials leading to an amplification is discussed and then we study the resulting spectrum and the dynamical features of the amplification for different potentials. The same study is then employed for the more general scenario of a non-minimally coupled inflaton, restricting the analysis, for simplicity, to the induced gravity case. In this context, we used the superpotential method to reconstruct the form of a potential leading to a spectrum amplification. In both cases, we build complete models of inflation that account for the constraints of CMB observations at larger scales and the requirements for PBH production at smaller scales. Finally, we compared the models analyzed to some of the recent PTA datasets analysis and we obtained that some inflationary models are mildly favoured w.r.t. others in fitting the constraints for the production of SIGW.