Structure of ensemble of cosmological models with dark energy

We show that all cosmological models which offer the explanation of the present acceleration of the Universe can be represented in terms of a fictitious particle moving in a one-dimensional potential parameterized by the scale factor or redshift. On the other hand this potential function can be reconstructed from SNIa data. From the potential function we can reconstruct the phase portraits and find that only models which are topologically equivalent to the ACDM model seems to be realistic models of the accelerating universe. We define the ensemble of dark energy models as a subspace of planar dynamical systems. We demonstrate that the ensemble can be structuralized by introducing the Sobolev metric. Then we obtain the Banach space structure of the ensemble. We investigate this ensemble in the context of the generic universe.