Topologia cósmica

Abstract

In this work we intend to discuss the topological and geometric structures of cosmological models. We begin with a review of differentiable manifolds, from the concept of topological manifolds to fundamental tools in Riemannian geometry. After that we present a classification of three-dimensional homogeneous spaces provided by Thurston, in 1982, focusing on constant curvature spaces and their respective fundamental polyhedra models. We also discuss the implications of the cosmological principle on the geometric structure of the FLRW model along with its divergences in terms of the anisotropy levels given by the CMB. Finally, we abandon the hypotheses responsible for the FLRW model in order to list the possible topologies of the spacial section of the spacetime. The importance of this work lies both on the rich structure behind cosmological models as well as on the value of a more rigorous treatment regarding our analysis on the topology of the Universe.