Large-scale CMB anisotropies in Silent Universes

In this thesis we explore a new approach to General Relativity introduced by G. Ellis in 197, that defined new dynamical equations (called relativistic hydrodinamical equations) based on the properties of the electric and magnetic parts of the traceless part of the Riemann tensor, the Weyl tensor. Matarrese et al. in the mid-1990s found new cosmological models, called silent universe, for the study of irrotational dust using the relativistic hydrodinamical equations, in which the magnetic part of the Weyl tensor vanishes. The small temperature anisotropies measured in the Cosmic Microwave Background (CMB) allow us to use the theory of cosmological perturbations. In particular we perturbed a Szekeres metric, in the form introduced by Goode and Wainwright in 1989, around a Friedmann-Lemaître-Robertson-Walker (FLRW) solution. This is a special silent universe that has an unique anisotropy along the z-axis. We solve the linearized Einstein Field Equations (EFE) in order to find the behaviour of the out-of-homogeneity potential and we study the phase plane analysis of this model using Ellis formalism. We study the geodesics equation for a photon path emitted on last scattering surface towards us. With the second-order solutions we compute the first and second-order CMB temperature anisotropies for the Szekeres metric. In the end we want to make explicit the expression of the first-order and second-order temperature deviation for a fully general silent metric, i.e. that contains the maximum degree of spatial anisotropy. In both cases we recover the integrated Sachs-Wolfe effect and a form that we interpret as the second-order correction of the integrated Sachs-Wolfe effect, both dependent on the direction of observation.