Homogeneous cosmologies and the Maupertuis-Jacobi principle
arXiv:gr-qc/0702058 · doi:10.1103/PhysRevD.75.107301
Abstract
A recent work showing that homogeneous and isotropic cosmologies involving scalar fields are equivalent to the geodesics of certain effective manifolds is generalized to the non-minimally coupled and anisotropic cases. As the Maupertuis-Jacobi principle in classical mechanics, such result permits us to infer some dynamical properties of cosmological models from the geometry of the associated effective manifolds, allowing us to go a step further in the study of cosmological dynamics. By means of some explicit examples, we show how the geometrical analysis can simplify considerably the dynamical analysis of cosmological models.
5 pages