Quantum Cosmology in Scalar-Tensorial Theories with Bohm-de Broglie Interpretation.

Name: Isaac Torres Sales
Type: PhD thesis
Publication date: 05/03/2020
Advisor:

Namesort descending Role
Oliver Fabio Piattella Advisor *

Examining board:

Namesort descending Role
Davi Cabral Rodrigues Internal Examiner *
Galen Mihaylov Sotkov Internal Examiner *
Jorge Zanelli External Examiner *
Júlio César Fabris Internal Examiner *
Nelson Pinto Neto External Examiner *
Oliver Fabio Piattella Advisor *

Summary: In this work, we both review and apply the formalism of Bohm-de Broglie interpretation of quantum mechanics to study two cosmological theories which modify Einstein’s general relativity through the introduction of a scalar field: the minimal and the non-minimal derivative couplings. We address some issues related to the quantization process in those theories, namely the ordering ambiguity and the problem of the quantization of Hamiltonians with non-integer powers in the momenta, in which case we apply a fractional derivative technique. We discuss how the Bohm-de Broglie interpretation provides us physical criteria to analyse the obtained results, specially with respect to the search for nonsingular solutions. With the help of those criteria, we discuss how the applied techniques are able to provide answers to the singularity problem, through bounces and cyclic universes.

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