Geometrizing the dynamics of Bianchi cosmology

The reparametrization freedom in the choice of time variable in the dynamics of spatially homogeneous cosmological models is used to reformulate the field equations as a geodesic flow for a "Jacobi geometry" in a particular time gauge called the Jacobi time gauge. For the diagonalizable models this Jacobi geometry is a conformally flat Lorentzian geometry. By choosing variables which are adapted to the symmetries of the Jacobi geometry, considerable simplification of the field equations is achieved, and one can explain the existence of all known exact solutions in terms of this analysis, as well as simplify the study of the qualitative behavior of the dynamics. In addition, certain "hidden symmetries" which arise in the Jacobi formulation lead to a class of new exact solutions.