Violação de Lorentz e teoria de gravitação modificada

Abstract

In this thesis we study the Lorentz and CPT symmetries breaking in a 4D fourfermions model at zero and at finite temperature. At zero temperature we find that these symmetries can be violated, but at finite temperature we show that there is a critical temperature at which the Lorentz and CPT symmetries are restored. We show that it is possible obtain the Friedmann equation in five dimensions in the presence of terms that violate the Lorentz symmetries , and as solution of this equation we find that the evolution of the universe is not usual, oscillating between accelerated phases and desaccelerated phases. We analyse the extension of the quantum eletrodynamics in the limit of high temperatures. Our aim is study the modifications that the Lorentz violation can cause in the free energy of the quantum eletrodynamics and with this to use experimental data related the free energy to estimate a numeric value to the parameter of Lorentz violation. We study a proposal of modification of the gravitation, this proposal consist in adding the Chern-Simons term to the usual gravitation. The issue most notable in this theory of gravitation is the search for solutions that occur in the general relativity and that somehow persist in this new theory. We show that for a given choice of scalar field that is introduced together with the Chern-Simons term, it is possible to find important solutions of the general relativity in this new theory of gravitation, as the Schwarzschild solution, the G¨odel metric, among others. We study with emphasis the G¨odel solution, showing that it is possible the existence this solution in the modified theory when we interpret the scalar field as a external field and when we interpret this same field as a dynamic field, this last interpretation leads the important modifications in parameter of the theory.