A dinâmica cosmológica do Modelo de Kantowski-Sach
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Data
2025-06-13
Autores
Silva, Breno Barreto da
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Universidade Federal do Espírito Santo
Resumo
In this thesis, we investigate the application of the homogeneous and anisotropic Kantowski-Sachs metric, characterized by two scale factors, in the construction of cosmological models alternative to the standard isotropic paradigm. To this end, we begin with a comprehensive review of the fundamentals of general relativity, relativistic hydrodynamics, and the Raychaudhuri equation, as well as an overview of the standard cosmological model, gathering the necessary elements for a consistent analysis of anisotropic scenarios. Initially, we revisit the original calculations of the Kantowski Sachs model, proposing a new graphical and interpretative approach to its dynamics. Subsequently, as an original contribution, we introduce a relation between the scale factors of the metric and obtain an exact solution of Einstein’s field equations, considering a general expression for the universe’s matter content, including the presence of a scalar f ield. We find that the presence of the scalar field leads to a significant decrease in energy density during the early stages, in a manner analogous to the inflationary process. Wealso determine the kinematic parameters associated with the model, such as the scalar expansion Θ, the shear σ, and the term RµνUµUν, related to the acceleration of the universe’s expansion. Finally, we analyze the evolutionary dynamics of the model through the Hubble, density, and deceleration parameters, aiming to understand the influence of anisotropy in a cosmological scenario with accelerated expansion.
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Kantowski-Sachs , Accelerated expansion , Kinematic parameters , Anisotropy , Raychaudhuri , Expansão acelerada , Parâmetros cinemáticos , Anisotropia