Singularidades cosmológicas no espaço-tempo de Weyl integrável: aspectos clássicos e quânticos

• Autor(a) principal: Barreto, Adriano Braga
• Data de Publicação: 2016
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/9567
• topic: Geometria de Weyl; Singularidades cosmológicas; Cosmologia quântica; Transformações canônicas; Weyl geometry; Cosmological singularities; Quantum cosmology; Canonical trans­formations; CIENCIAS EXATAS E DA TERRA::FISICA

We have investigated cosmological models governed by a geometrical scalar-tensor theory in the framework of the Weyl integrable manifolds. Such as theory corresponds to the general relativity, minimally coupled to a massless scalar field, in the frame where the geometry is riemannian. We present the fundamental elements of the Weyl geometry and we extend the hamiltonian formalism of the general relativity to this geometry. We propose a foliation invariant by Weyl transformations, in which the Weyl scalar field plays the role of a clock to measure the evolution of the foliation. Cosmological singularities are verified in the clas­sical solutions of the FLRW model and avoided in the quantum cosmology approach. The Weyl transformations provides a canonical transformations between two related frames and a unitary operator is defined to map these two frame in the quantum regime. The physical equivalence in the quantum level is discussed.