On early and late phases of acceleration of the expansion of the universe

This thesis tackles the vast question of generating accelerated periods of expansion of the universe. Models loosely related were developed in the early and late universe. In the early universe, generalizations of the Schwinger effect were developed in curved (de Sitter) space and some backreaction effects were estimated. In the late universe, a fractal model was developed and confronted to supernovae data. This relies on the idea of an accelerated expanding universe being nothing but a mirage due to inhomogeneities disposed in a fractal (in this particular model) way. Finally a model of interacting energy based on an Einstein-Cartan gravitational theory was phenomenologically investigated.