Related papers: A Closed Universe with Maximum Life-Time
We consider a multidimensional universe with the topology $M= \R\times M_1\times \cdots \times M_n$, where the $M_i$ ($i>1$) are $d_i$-dimensional Ricci flat spaces. Exploiting a conformal equivalence between minimal coupling models and…
In this paper, we consider the application of optimal periodic control sequences to switched dynamical systems. The control sequence is obtained using a finite-horizon optimal method based on dynamic programming. We then consider Euler…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
Setting aside anthropic arguments, there is no reason why the universe should initially favour a net expanding phase rather than one experiencing a net contraction. However, a collapsing universe containing "normal" matter will end at a…
We extend the cosmological predictions from assuming the total action of the universe is finite. When initial and final singularities in curvature invariants are avoided, it leads to singularities in the gravitational action of the…
A general effective field theory formalism is presented which describes the low-energy dynamics of a 3-brane universe. In this scenario an arbitrary four-dimensional particle theory, such as the Standard Model, is constrained to live on the…
The core problem in optimal control theory applied to quantum systems is to determine the temporal shape of an applied field in order to maximize the expectation of value of some physical observable. The functional which maps the control…
This paper develops constraints on the values of the fundamental constants that allow universes to be habitable. We focus on the fine structure constant $\alpha$ and the gravitational structure constant $\alpha_G$, and find the region in…
We study a model that the entropy per particle in the universe is constant. The sources for the entropy are the particle creation and a lambda decaying term. We find exact solutions for the Einstein field equations and show the compatibilty…
We present a new approach to constructing inflationary models in closed universes. Conformal embedding of closed-universe models in a de Sitter background suggests a quantisation condition on the available conformal time. This condition…
Using a single dilaton field, a unified model of the Universe is proposed, which evolves from the radiation-like dominance in the Big Bang, to the dark-matter-like dominance in the early Universe, to the coexistence of both dark-matter-like…
In a Brans-Dicke (BD) cosmological model, the energy density associated with some scalar field decreases as $\displaystyle a^{{-2}(\frac{\omega_{o}+ {\frac12}%}{\omega_{o}+1})} $ with the scale factor $a(t)$ of the Universe, giving a matter…
We try to find conditions, the fulfillment of which allows a universe born in a metastable false vacuum state to survive and not to collapse. The conditions found are in the form of inequalities linking the depending on time $t$…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…
In this article we study closed inflationary universe models using the Gauss-Bonnet Brane. We determine and characterize the existence of a universe with $\Omega > 1$, with an appropriate period of inflation. We have found that this model…
If the effective cosmological constant is non-zero, our observable universe may enter a stage of exponential expansion. In such case, regions of it may tunnel back to the false vacuum of an inflaton scalar field, and inflation with a high…
The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a…
An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A…
Exact solutions for a model with variable $G$, $\Lambda$ and bulk viscosity are obtained. Inflationary solutions with constant (de Sitter-type) and variable energy density are found. An expanding anisotropic universe is found to isotropize…