# Quantum cosmology in scalar-tensor theories: physical and mathematical aspects.

Name: Carla Rodrigues Almeida

Type: PhD thesis

Publication date: 21/09/2017

Advisor:

Name | Role |
---|---|

Júlio César Fabris | Advisor * |

Examining board:

Name | Role |
---|---|

Antonio Brasil Batista | Internal Examiner * |

Davi Cabral Rodrigues | Internal Examiner * |

José Alexandre Nogueira | Internal Examiner * |

Júlio César Fabris | Advisor * |

Nelson Pinto Neto | External Examiner * |

Oliver Fabio Piattella | Internal Examiner * |

Santiago Esteban Perez Bergliaffa | External Examiner * |

Summary: The proposal of this work is to study the mathematical and physical aspects of the canonical quantization of scalar-tensor theories, Brans-Dicke Theory in particular, using a perfect fluid as the universe's matter component, inserted by Schutz's formalism. We do a thorough analysis of the self-adjointness of the effective energy operator obtained

in the quantization of theory. Such quantization is made through the Wheeler-DeWitt equation, the energy constraint from the Hamiltonian description of General Relativity, to obtain a Schrödinger-like equation, taking the temporal parameter to be given by the fluid that permeates the universe. We adopt the Copenhagen Interpretation of Quantum

Mechanics to analyse the quantized system. Also, we present the quantization of the K-essence Theory, for a particular limit which we recover a perfect fluid behavior from General Relativity by Schutz. We also introduce the notion of affine quantization as an alternative to the canonical method, and present the mathematical concepts needed for

the theory. We apply this method in a cosmological example, of a universe filled with dust. Also, we do a qualitative semiclassical analysis of the Brans-Dicke Theory.