Formação de estruturas em cosmologia no regime não-linear: uma aproximação por sistemas dinâmicos

Abstract

The formation of large scale structure is an outstanding problem in Cosmology. It is a consensus that the observed variety of structures such as galaxies and clusters of galaxies have originated from small fluctuations of the cosmic fluid possibly generated during the inflationary epoch-in the matter dominated era. The early stages of evolution of these fluctuations are described by the Jeans theory resulting from the linear approximation of the hydrodynamical equations. Basically, the instabilities due the action of the gravitational field induce the existence of two types of perturbativo modes: the unstable modes that grow, and the stable one that oscillate as sound waves. The distinction between these modes depend son whether the wave length of a given perturbativo mode is greater or smaller than atypical wave-length known as the Jeans length. Eventually, the growth of the unstable modes breaks the linear approximation and nonlinear effects turn out to be crucial for the formation of structures. In this vein, our objective here is to study the problem of nonlinear structure formation in a matter dominated expanding universe considering a consistent extension of the linear Jeans theory. A dynamical system approach is provided by the Galerkin method used to integrate the self-gravitating fluid dynamical equations. Therefore, the behavior of the unstable and stable perturbative modes of the cosmic fluid are exhibited beyond the linear regime prior the formation of structures. We have also considered the influence of viscosity consistently rather than introducing it in an artificial way as in the Adhesion Model.