Related papers: A Closed Universe with Maximum Life-Time
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related…
It is proven that any spherically symmetric spacetime that possesses a compact Cauchy surface $\Sigma$ and that satisfies the dominant-energy and non-negative-pressures conditions must have a finite lifetime in the sense that all timelike…
In this talk we present a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field and a cosmological constant. Our results confirm the possibility of a collapsing universe (for a given…
We discuss cosmological models for an eternal universe. Physical observables show no singularity from the infinite past to the infinite future. While the universe is evolving, there is no beginning and no end - the universe exists forever.…
The maximum size of a bound cosmic structure is computed perturbatively as a function of its mass in the framework of the cubic galileon, proposed recently to model the dark energy of our Universe. Comparison of our results with…
A highly excited Friedmann universe filled with a scalar field and radiation has been considered. On the basis of a direct solution to the quantum-mechanical problem with a well-defined time variable, it has been shown that such a universe…
A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…
Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically,…
We propose a cosmological model in which the universe undergoes an endless sequence of cosmic epochs each beginning with a `bang' and ending in a `crunch.' The temperature and density are finite at each transition from crunch to bang.…
The expansion of the closed two-component universe has been considered. The potential barrier of the expansion has been investigated and its overcoming condition has been obtained. The restrictions on the Friedmann integrals, cosmological…
Current observations of the fraction of dark energy and a lower limit on its tension, coupled with an assumption of the non-convexity of the dark energy potential, are used to derive a lower limit of 26 billion years for the future age of…
We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has new surprising features. The universe is ``closed'' in the…
We investigate the string configuration that, in the framework of the theoretical scenario introduced in [1], corresponds to the most entropic configuration in the phase space of all the configurations of the universe. This describes a…
A new class of exact solutions of Einstein's field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations…
A dynamical correspondence is established between positively curved, isotropic, perfect fluid cosmologies and quasi-two-dimensional, harmonically trapped Bose-Einstein condensates by mapping the equations of motion for both systems onto the…
In this work we present a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field and a cosmological constant. Our results confirm the possibility of a future collapsing universe (for a…
We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of…
The Hubble constant, which measures the expansion rate, together with the total energy density of the Universe, sets the size of the observable Universe, its age, and its radius of curvature. Excellent progress has been made recently toward…
We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…