Methods of continuous topological evolution and topological thermodynam-ics are used to construct a cosmological model of the present universe, using the techniques based upon Cartan’s theory of exterior differential systems. Thermo-dynamic domains, which are either Open, Closed, Isolated, or in Equilibrium, can be put into correspondence with topological systems of Pfaff topological dimen-sion 4, 3, 2 and 1. If the environment of the universe is assumed to be physical vacuum of Pfaff topological dimension 4, then continuous but irreversible topolog-ical evolution can cause the emergence of topologically coherent defect structures of Pfaff topological dimension less that 4. As galaxies and stars exchange radia-tion but not matter with the environment, they are emergent topological defects of Pfaff topological dimension 3 which are far from equilibrium. It is conjectured that dark matter and energy is represented by those thermodynamic topological defect structures of Pfaff dimension 2 or less; such structures do not exchange radiation or matter with the environment; hence they would not be observed electromagnetically, but they could influence gravitational dynamics. DeRham topological theory of period integrals over closed but not exact exterior differen-tial systems leads to the emergence of quantized, deformable, but topologically coherent, macrostates at all scales.
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