Non-Minimally Coupled Cosmology as Geodesic Motion

Recent works showing that homogeneous and isotropic cosmologies involving scalar fields correspond to geodesics of certain augmented spaces are generalized to the non-minimal coupling case. As the Maupertuis-Jacobi principle in classical mechanics, this result allows us, in principle, to infer some of the dynamical properties of the cosmologies from the geometry of the associated augmented spaces.