Lecture Notes on Gauge Theories and Inhomogeneous Cosmologies

These lecture notes were meant to compile the main ideas on gauge field theory and modern cosmology, showing the recent contributions of the author in these areas, including classical thermodynamics, supergravity and quantum gravity. Although the author has conducted the work without wishing to exhaust the issues in question, this synthesis provides some essential formal approaches for further studies, with relevant and updated references, as well as indications of classical readings. Special attention was given to the application of Lyra's geometry, because of its growing importance in quantum cosmology, and to the so-called < >, a model of supergravity developed by the author with the purpose to offer a classical representation for supergravity that could be made compatible with the quantum theory of spacetime also developed by himself. Also in general cosmology, the emphasis was on inhomogeneous models due to the debate they open on the validity of the standard model. In this sense, the author presented his perturbative formalism of weak gravitational lensing by defining an inhomogeneous cosmological refractive index within a Lemaître-Tolman universe. Lastly, some remarks on Stephani cosmology were organized in order to expose the most significant features of this approach. During the reading, it shall be possible to observe some title marks indicating items of interest, as well as small side texts with outgivings of renowned authors.Key words: gauge field theory, cosmology, Lyra's geometry, quantum gravity, supergravity.====================================================================================================== A presente coletânea de notas de aula foi organizada como compilação das principais idéias sobre teoria de campo de calibre e cosmologia moderna, mostrando as recentes contribuições do autor nessas áreas, incluindo termodinâmica clássica aplicada, supergravidade e gravitação quântica. Embora o trabalho tenha sido conduzido sem pretensões a esgotar os temas em apreço, a síntese ...