Phd in PHYSICS

Thesis title: Classical and quantum study of the Big Bounce in Early Cosmology

The presence of spacetime singularities is a very general property of the Einstein equations, as demonstrated by the renowned Singularity Theorems by Hawking and Penrose in \cite{PH1,PH2}. This might be the sign that General Relativity loses its predictability near the Planckian region and that a quantum theory of gravity is required in order to solve the non-physical predictions of the Einstein theory out of its range of validity. The Big Bounce, as first derived in Loop Quantum Cosmology, represents the most successful scenario in which the initial singularity of our Universe is solved thanks to the emergence of quantum gravity effects at the Planck scale (see also \cite{OtherBounce1,OtherBounce2,F1,F2,F3}, in which a bouncing scenario is due to a modified classical dynamics). This thesis aims at studying the quantum Big Bounce by characterizing both its quantum features and the semiclassical ones, the latter resulting in a modified Einsteinian picture. We face this study by analyzing many different cosmological scenario, mainly with the tools of Polymer Quantum Mechanics and the Generalized Uncertainty Principle representation, and by proposing a new paradigm for a Quantum Big Bounce. Throughout the paper, we address some issues and discuss outstanding questions.