A Topological Perspective of Cosmology

R.M. Kiehn
Emeritus, Physics Dept.
Univ of Houston
69 chemin Saint Donat
84380 Mazan France
Phone: 04-90-69-61-25 (in France)
Email: rkiehn2352@aol.com

http://www22.pair.com/csdc/pdf/cosmos.pdf

ABSTRACT: Methods of continuous topological evolution, expressed in terms of Cartan's theory of exterior differential forms, are used to construct a cosmological model of the present universe. The methods invoke topological, non-statistical, thermodynamic principles without geometric constraints of metric, connection or gauge. Stars and galaxies appear as self organizing topological defects, or condensates, of Pfaff topological dimension 3, embedded in a turbulent dissipative, but very dilute, non-equilibrium medium of Pfaff topological dimension 4. Such defects form long lived states of Pfaff dimension 3, and as such are states far from equilibrium which are of Pfaff topological dimension of 2 or less. The Jacobian matrix of the 1-form of Action used to describe the physical system leads to a universal phase function as a characteristic polynomial of fourth degree. The similarity invariants of the Jacobian matrix may be used to express the holomorphic polynomial in an intrinsic manner. The phase function can be interpreted as a family of implicit surfaces in an intrinsic 4D space, with a complex family, or order, parameter. The envelope of the family is homeomorphic to the Gibbs swallowtail surface of a van der Waals gas. The singular set of the family is homeomorphic to the equation of state of a van der Waals gas. The implication is that a domain of Pfaff topological dimension 4 can be deformed into a representation that mimics a van der Waals gas. If the gas is near its critical point, there are large fluctuations in density, which Landau has shown are correlated with a 1/r? attractive force. Hence, a cosmological model based on the assumption that the universe is a dilute, non-equilibrium turbulent gas near its critical point explains the the granularity of the night sky, the inverse square law of gravitation, and the expansion of the universe.