Dottorato in FISICA

Titolo della tesi: Effects and Phenomenology of Cut-Off Physics on the Primordial Universe

The main focus of this thesis is the implementation of alternative quantization procedures, developed to easily introduce quantum gravitational corrections, on cosmological models. The aim is to study the fate of cosmological singularities and to derive possible signatures of more fundamental Quantum Gravity theories. Polymer Quantum Mechanics (PQM) is a procedure of quantization on a lattice, inspired by Loop Quantum Gravity but derived independently. The discretization of a position-like variable implies a cut-off on the corresponding momentum, and its implementation on the cosmological minisuperspaces, called Polymer Cosmology, is usually able to remove the Big Bang and Big Crunch singularities, replacing them with a Big Bounce similarly to Loop Quantum Cosmology. However the properties of the Bounce, i.e. its universality or its dependence on initial conditions, depend on the geometrical nature of the variable chosen to describe the model. After a comparison of different sets of variables in the isotropic Friedmann-Lema\^itre-Robertson-Walker model, the privileged variable to obtain a universal Bounce is identified in the cubed scale factor corresponding to the comoving volume. The recovery of the equivalence between different sets of variables after the discretization has been implemented is still an open question, and it can have implications for Loop Quantum Cosmology. The Generalized Uncertainty Principle representation (GUP), inspired by String Theories, introduces higher-order corrections on the canonical commutation relations and implies an absolute minimal uncertainty on position. Its cosmological implementation however is not usually able to remove the singularities; furthermore, the recreation of Brane Cosmology (a cosmological sector of String Theories) happens only for a different variation of this representation. Indeed, it is possible to extend the GUP formulation to different functions of the momentum, obtaining deformed commutation relations known as Modified Algebras. Not all of them imply minimal uncertainties, but some can introduce energy cut-offs. In particular, there are specific formulations able to reproduce Polymer Cosmology and Brane Cosmology. Another interesting form is able to remove singularities not through a Bounce but through an asymptotic behaviour; this way it is possible to reproduce the so-called Emergent Universe model without the fine tuning needed on a classical level. Modified Algebras can be used to easily derive corrections to the primordial Power Spectrum of scalar perturbations, thus yielding a possibly observable signature of quantum gravitational corrections. When applied to the gravitational collapse of a dust cloud, they are able to halt the collapse and prevent the formation of Black Holes, thus possibly explaining the recently observed violations of star mass limits. This thesis represents a starting point for the development of alternative quantization procedures as a somewhat phenomenological approach to implement corrections from more fundamental Quantum Gravity theories. There is still the need to define and develop canonical transformations between different sets of variables, since at the moment they seem to yield inequivalent dynamics; furthermore, the algebras can have different operatorial representations whose equivalence must still be formally proven. Finally, their implementation on more complex systems such as the anisotropic and chaotic Bianchi IX model or inhomogeneous solutions could be useful towards the further development of a complete theory of Quantum Gravity.