Quantum to Classical transition in the early Universe: models and observational signatures

Inflation is the standard scenario for the Early Universe providing a mechanism to explain the generation of primordial density perturbations from which all the structures we see in the universe formed by subsequent gravitational growth (like, e.g., anisotropies of the Cosmic Microwave Background, or the large-scale distribution of galaxies). The inflationary seeds for structure formation are traced back to quantum fluctuations of one or more (scalar) fields. However galaxies or cluster of galaxies do behave as classical objects. This entails the issue of understanding a quantum-to-classical transition in a cosmological framework. From this point of view inflation and cosmological observations can represent an interesting laboratory to explore some issues related to the quantum measurement problem. This issue has been long known, still it has been not explored in full details, and recently there has been a renowned interest in it. The thesis will consist in a first part of review of the most recent studies on the subject. It will then focus on some aspects of the problem, namely how the classical to quantum transition impacts on primordial gravitational waves which are a smoking gun of inflation, and whether and how such a transition can leave specific signatures in cosmological observables that go beyond the usual analyses (such as, e.g., non-Gaussianity of the cosmological perturbations from inflation).