Cosmologia quântica em teorias escalares-tensoriais: aspectos físicos e matemáticos.

Abstract

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 Schr¨odinger-like equation, taking the temporal parameter to be given by the fluid that permeates the universe. 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.