  As a point of departure it is suggested that Quantum Cosmology is a
topological concept independent from metrical constraints. Methods of
continuous topological evolution and topological thermodynamics are used to
construct a cosmological model of the present universe, using the techniques
based upon Cartan's theory of exterior differential systems. Thermodynamic
domains, which are either Open, Closed, Isolated, or in Equilibrium, can be put
into correspondence with topological systems of Pfaff topological dimension 4,
3, 2 and 1. If the environment of the universe is assumed to be a physical
vacuum of Pfaff topological dimension 4, then continuous but irreversible
topological evolution can cause the emergence of topologically coherent defect
structures of Pfaff topological dimension less than 4. As galaxies and stars
exchange radiation but not matter with the environment, they are emergent
topological defects of Pfaff topological dimension 3 which are far from
equilibrium. DeRham topological theory of period integrals over closed but not
exact exterior differential systems leads to the emergence of quantized,
deformable, but topologically coherent, singular macrostates at all scales. The
method leads to the conjecture that dark matter and energy is represented by
those thermodynamic topological defect structures of Pfaff dimension 2 or less.
