Modelos Simples de Lemaitre - Tolman - Bondi (LTB) - Isidro, Eddy Giusepe Chirinos (2015)
The current standard model of cosmology, the ?CDM model (?-Cold Dark Matter), is on the homogeneous solutions of Friedmann-Lemaître-Robertson-Walker (FLRW) of Einstein’s equations. The characteristics of the Cosmic Microwave Background (CMB) and structure formation on large scales are studied through the theory of cosmological perturbations in homogeneous and isotropic background. However, in the last fifteen years, "simple" inhomogeneous cosmological models that are generalizations of FLRW cosmological model gained interest in astrophysics community and have been used to study cosmological phenomena. Some authors have shown that these inhomogeneous models with spherical symmetry and dust source can play a good fit for the data type Ia supernovae (SNIa) and the position of the first peak of the CMB. These models suggest that the apparent accelerated expansion of the universe is not caused by the repulsive gravity due to dark energy, but is rather a result of inhomogeneities in the distribution of matter. In this dissertation, inhomogeneous models of the Universe are investigated on the basis of Lemaître-Tolman-Bondi (LTB) metric, which represents a spherical symmetry solution to dust. Two particular models are studied: the parabolic evolution with inhomogeneous Big Bang’s time and the of hyperbolic evolution with weak curvature and constant Big Bang’s time. The properties of each of these models are investigated in detail, as analitically as possible. Both models are compared with astrophysical observations of the sample Union2.1 SNIa. It is conclude that these models could be a starting point to develop more realistic models. Thus LTB solution is capable to explain the observed relationship between distance luminosity and redshift of supernovae without the requirement of dark energy when the inhomogeneity is either the form of an empty or there is a hill centered on the observer; with the further assumption that the outside Universe, in both cases, is approxinately described by the Einstein-de sitter homogeneous model.