Homogeneous and isotropic world models in the Yang–Mills dynamics of gravity. The structure of the adiabats

Abstract

The time evolution of homogeneous and isotropic matter distributions is analyzed for the restricted Yang–Mills curvature dynamics of gravity. This theory of gravity is a tidal dynamics for which relativistic matter in detailed balancing cannot produce tidal forces. It defines a dynamical system on the curvature plane spanned by the two components of the Riemann curvature of Robertson–Walker space–times; the essential features of the cosmological solutions are presented by means of their phase portraits in the curvature plane. In the asymptotic limit (S→∞) the phase portrait, which in general depends on the equation of state and on the change of the entropy per particle, is structurally stable under the transition from Einstein’s dynamics to the Yang–Mills dynamics for any realistic equation of state. The phase portraits are explicitly constructed for the equation of state p=nρ, 0≦n≦1, and constant entropy per particle. A criterion for the existence of regular trajectories is given for the full Yang–Mills dynamics including entropy production. Finally, we discuss the relations between the observational parameters.