On globally static and stationary cosmologies with or without a cosmological constant and the dark energy problem

In the framework of spatially averaged inhornogeneous cosmologies in classical general relativity, effective Einstein equations govern the regional and the global dynamics of averaged scalar variables of cosmological models. A particular solution may be characterized by a cosmic equation of state. In this paper, it is pointed Out that a globally static averaged dust model is conceivable without employing a compensating cosmological constant. Much in the spirit of Einstein's original model we discuss consequences for the global, but also for the regional properties of this cosmology. We then consider the wider class of globally stationary cosmologies that are conceivable in the presented framework. All these models are based on exact solutions of the averaged Einstein equations and provide examples of cosmologies in all out-of-equilibrium state, which we characterize by all information-theoretical measure. It is shown that such cosmologies preserve high-magnitude kinematical fluctuations and so tend to maintain their global properties. The same is true for a A-driven cosmos in such a state despite exponential expansion. We outline relations to inflationary scenarios and put the dark energy problem into perspective. Here, it is argued, on the grounds of the discussed cosmologies, that a classical explanation of dark energy through backreaction effects is theoretically conceivable, if the matter-dominated universe emerged from a non-perturbative state in the vicinity of the stationary solution. We also discuss a number of caveats that furnish strong counter arguments in the framework of structure formation in a perturbed Friedmannian model.