Classification of Cosmological Trajectories
  In the context of effective Friedmann equation we classify the cosmologies in multi-scalar models with an arbitrary scalar potential $V$ according to their geometric properties. It is shown that all flat cosmologies are geodesics with respect to a conformally rescaled metric on the `augmented' target space. Non-flat cosmologies with V=0 are also investigated. It is shown that geodesics in a `doubly-augmented' target space yield cosmological trajectories for any curvature $k$ when projected onto a given hypersurface. 
Qi Guo, Rong-Gen Cai