Search

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.

Starting from Einstein's equations of the Classical General Relativity, new kinds of solutions for the Mixmaster model are explored. By dispensing with the extension to the complex variable field, which is usual in problems such as the Laplace equation or the harmonic oscillator, in a similar manner to that of Quantum Mechanics, the equations appear to have solutions that belong to the complex General Relativity. A first integral is performed by establishing a separation of the first derivatives. Then a second integral is obtained once the respective equations with separate variables are found and whose integrals provide a family of complex solutions. However, reality conditions do not seem to be easily imposed at this stage. Above all, it is significant that the classical Einstein's equations for the debatably integrable Mixmaster model present complex solutions.

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.

A work, recently published by this journal, is discussed and the critique is presented in this same issue. Our revision of this critique is focused on two main topics: a) the suggested Taub solution and (b) the method followed to arrive at it.

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.

The space-space field equations of the Jordan Brans-Dicke theory describing a spatially homogeneous vacuum spacetime of the Bianchi type can be brought under transformation into a general set of nonlinear differential equations, an all-encompassing general equation implicitly contained in each of the cosmological models studied, most of whose analytic solutions the authors have found. The scalar field displays a considerable influence in the cosmological context during the early, strongly relativistic stage of the universe's expansion where the main difference between the cosmologies of Einstein general relativity and Jordan Brans-Dicke theories lies in the possible existence of a sourceless phi field which, since it is not generated by matter, is contrary to Mach's principle. Several solutions presented are reported for the first time.

We present two methods for solving the cosmological equations of the scalar-tetradic theory B [19] when a Friedmann-Robertson-Walker (FRW) geometry is assumed. Among the many solutions found there are several physically meaningful ones including inflationary universe solutions.

The cosmic, general analitic solutions of the Brans--Dicke Theory for the flat space of homogeneous and isotropic models containing perfect, barotropic, fluids are seen to belong to a wider class of solutions --which includes cosmological models with the open and the closed spaces of the Friedmann--Robertson--Walker metric, as well as solutions for models with homogeneous but anisotropic spaces corresponding to the Bianchi--Type metric clasification-- when all these solutions are expressed in terms of reduced variables. The existence of such a class lies in the fact that the scalar field, $\phi$, times a function of the mean scale factor or ``volume element'', $a^3 = a_1 a_2 a_3$, which depends on time and on the barotropic index of the equation of state used, can be written as a function of a ``cosmic time'' reduced in terms of another function of the mean scale factor depending itself again on the barotropic index but independent of the metrics here employed. This reduction procedure permites one to analyze if explicitly given anisotropic cosmological solutions ``isotropize'' in the course of their time evolution. For if so can happen, it could be claimed that there exists a subclass of solutions that is stable under anisotropic perturbations., Comment: 15 pages, Latex

En la primera parte de este trabajo se obtiene la solución analítica a un problema cosmológico largamente discutido. Partiendo de las ecuaciones de Einstein de la Relatividad General clásica se encuentran soluciones para el modelo de universo Mixmaster, que pertenecen a la Relatividad General compleja. La estrategia se basa en buscar primero una separación de las primeras derivadas, para posteriormente obtener las ecuaciones diferenciales con variables separadas. Las condiciones de realidad se imponen de manera directa sobre el tiempo cosmológico. Finalmente, cabe señalar lo significativo que resulta, que las ecuaciones de Einstein clásicas para el modelo de universo Mixmaster, cuya integrabilidad ha sido extensamente discutida, presenten soluciones complejas. En la segunda parte de este trabajo, a través de una estrategia particular de separación de variables en el tiempo cosmológico, se encuentra una nueva familia de soluciones de las ecuaciones de Einstein para el modelo de universo de Taub, mucho más general que la solución conocida. Entre las características de las nuevas soluciones se destaca el fenómeno de la anti gravedad. Este fenómeno anti gravitatorio convierte al universo de Taub en un universo acelerado.