In 1965 after rereading Landau's satistical derivations, I made the conjecture
that if the universe was a very dilute ideal gas near its critical point, and
the condensation fluctuations were the stars and galaxies, then the cosmological
model of a very dilute gas near the critical point gave a simple explanation for
the granularity of the night sky, and for the attractive gravitational force
law. Such results are not inherent in the homogeneous metrical models of
current general relativity theory. When Cartan's methods of exterior differential forms are applied to the study of thermodynamics, it appears that on a space time of 4 geometric dimensions, a turbulent nonequilibrium open thermodynamic system can exist and will be of Pfaff topological dimension 4. Processes that are initialized in such a turbulent state can decay to closed thermodynamic states of Pfaff dimension 3, and thereby create long lived topological defects representing stationary states far from equilibrium. (Equilibrium requires a Pfaff dimension of 2 or less).
When the universe is represented by an exterior differential 1form of Pfaff
topological dimension 4, the Jacobian matrix has a CayleyHamilton
characteristic polynomial of degree 4. At the system evolves, one of the
eigenvalues of the characteristic equation can approach zero, which will reduce
the Pfaff topological dimension to 3. The resulting cubic polynomial
constructed from the similarity invariants of the Jacobian have a representation
as a universal van der Waals gas. The remaining eigen values of the
characteristic polynomial can be complex, which would describe a nonequilibrium
van der Waals gas. The critical point can be determined in terms the similarity
invariants (curvatures) of the Jacobian matrix.
