Análise geométrica e dinâmica de modelos de gravidade generalizada / Geometrical and Dynamical Analysis of Generalized Gravity Models

AUTOR(ES)

José Cleriston Campos de Souza

DATA DE PUBLICAÇÃO

2008

RESUMO

This work aims the investigation of some dynamical aspects of generalized gravity models, namely scalar-tensor and f(R) models. These models intend to solve in a more natural way the problem of the existence of the dark energy, which is supposedly the component of the Universe that causes its accelerated expansion. In a null spatial curvature Friedmann-Lemaître-Robertson-Walker spacetime, it has been possible to write the equations of movement in a fashion that allowed us to obtain a dynamical system with a reduced number of variables, whose phase space has been generically studied and depicted for some particular models. In sequence, the dynamically forbidden regions and the fixed points of the phase space have been analyzed. For f(R) models, we have presented effective Lagrangians and Hamiltonians and derived a general expression for the equation of state parameter w. Furthermore, we have discussed the equivalence between f(R) and scalar-tensor models. Finally, we have introduced the Maupertuis-Jacobi Principle, which allows one to relate the Lagrangian for a mechanical system to a metric in a certain Riemannian manifold, to determine singularities which may appear in f(R) models, in an isotropic metric as well as in an anisotropic one of the simplest kind (Bianchi type I). We have found, in a more direct way, the same singularities that arise by using dynamical analysis methods.

ASSUNTO(S)

gravitation maupertuis-jacobi principle cosmologia dynamical analysis generalized gravity gravitação gravidade generaliza princípio de maupertuis-jacobi análise dinâmica cosmology

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