Cosmology and the Maupertuis-Jacobi principle / Cosmologia e o principio de Maupertuis-Jacobi
AUTOR(ES)
Luciana Aparecida Elias
DATA DE PUBLICAÇÃO
2008
RESUMO
We will show that the equations of motion for a class of non-minimally coupled anisotropic scalar-tensorial cosmological models are equivalent to the geodesic fux on certain augmented manifold endowed with a non-Riemannian metric. This result generalizes some recent ones and provides a better dynamical classification of the phase space of such cosmological models. The techniques employed in this work are, basically, a generalization of the well known Maupertuis- Jacobi Principle of Classical Mechanics, which allows us to associate the geodesic flux of a particular metric (the so called Jacobi Metric) to the equations of motion of a given mechanical system, typically a Hamiltonian one. We will show also that the classical geometrical approach based on the Eisenhart metric can be generalized in an analogous way for the cosmological case, leading to another complementary geometrical approach to that one corresponding to the generalization of the Maupertuis-Jacobi Principle. Such results are applied to certain quintessential cosmological models leading to some interesting and promising results
ASSUNTO(S)
geodesica (matematica) geodesics (mathematics) quintessencia quintessence cosmology cosmologia
