Thermodynamics and quantum cosmology -- Continuous topological evolution of topologically coherent defects

Abstract

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.