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Following a specific strategy in which the cosmological time variables are operated upon, a new family of solutions to the empty Taub universe is found. Among the characteristics of such a family, it stands the positive acceleration provided by the tri-curvature property of this universe to two of the three scale factors of the Taub model. This effect of the tri-curvature results not in a restoring force such as normal gravity but in the conversion of the Taub cosmology into an accelerating universe.

We discuss the dynamics of anisotropic Bianchitype IX models in Jordan-Brans-Dicke cosmological theoryrendering the evolution of a universe model with closedspace near its beginning before inflation sets in. This paper displays how, when writtenin terms of reduced variables, the field equations allowstraightforward partial integration. The mean expansionH, the scalar field, and the three scale factors aregiven in terms of the volume expansion.

Given the extreme difficulty in finding analytical solutions to Einstein’s equations for universe models, such as the Bianchi type IX, different physical-mathematical techniques have been designed to attempt to find, at least approximate solutions that could have relevance in modern cosmology. Belinskii, Khalatnikov and Lifshitz (BKL) have developed a method to study a particular time evolution dynamic of the Bianchi type IX universe model. Herein, it is shown that this method contains pitfalls. These pitfalls, among other things, prevent the conclusion that this model provides chaotic behaviour. We show that the initial presumption made by BKL turns out to be inconsistent with the assumed initial conditions, since it cannot be kept along with the time-extended BKL process. That is, the Kasner stipulations corresponding to τ→∞, taken as initial conditions, are at odds with the initial assumption imposed on Einstein’s field equations.

The dynamics of the production of relative high frequency gravitational waves by astrophysical events taking place within the galaxies in the cosmological context can be well represented by a phenomenological description of the generating processes through a “radiation energy profile” that contains two adjustable parameters. This profile gives a relation between the total pressure and energy density of the matter generating gravitational radiation together with the “waves” themselves, both treated as ordinary hydrodynamic fluids. The resulting cosmological models then represent, in a descriptive way only, universes filled with two interacting fluids: on the one hand gravitational radiation, and the matter which emits it but does not reabsorb it, on the other. It is shown that the dynamic effects of the model can be significant, even if the conversion rate of matter into gravitational radiation is relatively small.