Cosmologia de universos emergentes de Mundos-Brana - Strey, Frederico Luiz (2018)
We consider some problems related to cosmological brane-world models, with an extra noncompact fifth dimension. We investigate different options for geometrical terms representing 2- and 1-branes immersed in a 3-brane universe. The latter is embedded in a 5-dimensional space-time corresponding to a black hole in AdS5. We show that the net effect of the inclusion of lower dimensional brane-gas terms consists in a rather specific form of the efective density of the matter fluid filling the emergent 3-brane universe. This turns out to present the elements of the standard cosmological model: radiation, dust and a positive cosmological constant, but it also has two additional terms corresponding to a string gas and a brane gas. The main problem studied in the present work concerns the detailed description of all the possible evolutions of the homogeneous and isotropic 3-brane universe, depending crucially on the different classes of admissible initial conditions, determined by the specific relations between the cosmological parameters. Even if the form of the induced matter fluid is unchanged, we have shown that in the most simple example (i.e. without dust) there exists eleven families of qualitatively different cosmological histories. The methods we have used in the description of the properties of the evolution of the 3-brane universes include analysis of dynamical systems, as well as the construction of the exact form of the solutions of the FRW equations (when it is possible), presenting the scale factor and the scalar field as explicit functions of cosmic time. In all these cases, the origin of the differences between the observed eleven different universe evolutions (and of the phase transitions between them) consists in the existence of fixed point and fixed lines of the planar dynamical system, due to the qualitatively different inicial conditions and of the different forms of the potential of the scalar field.