Yang-Mills driven Cosmic Expansion

Abstract: This thesis will investigate the possibility to have SU(2) gauge fields as the source to the Cosmic Inflation and/or to the Dark Energy. It will be explained that, under certain conditions, the Universe can be filled with vector fields without violating its isotropy. Those conditions are naturally fulfilled within the SU(2) gauge theory. Both Einstein's equations and the equations of motion for the fields will be found from the first principles. The equations will be used to show that classical SU(2) gauge fields behave as radiation and can therefore not cause an exponential expansion. But when vacuum polarizations is taken into account the fields, in the one-loop approximation, behave as a constant energy density which indeed can drive an exponential expansion of the Universe. First order perturbations in classical SU(2) gauge fields and in the space-time will be considered. The main purpose for that is to put up a framework in which it is possible to extract predictions of how the fluctuations in the energy density would be distributed over space. Firstly, it will be shown that for perturbations in the framework of Chaotic Inflation there is only one degree of freedom; one invariant combination of the perturbations in the space-time. The invariant combinations for classical SU(2) gauge fields has not been found in this theses but it is shown that neither the invariant in the Chaotic Inflation nor the Bardeen variables are invariant for those fields. The fluctuations in the energy density will be calculated numerically in the synchronous gauge for classical SU(2) gauge fields. The result shows that there will be an energy transfer from the homogeneous part of the fields to the fluctuations; both in the fields themselves and in the space-time. Since in a full quantum description the fluctuations correspond to particles, this describes a mechanism for particle production.