A closed-form solution in a dynamical system related to Bianchi IX

The Bianchi IX cosmological model in vacuum can be represented by several six-dimensional dynamical systems. In one of them we present a new closed form solution expressed by a third Painlevé function.     

Cosmological models with fluid matter undergoing velocity diffusion

A new type of fluid matter model in general relativity is introduced, in which the fluid particles are subject to velocity diffusion without friction. In order to compensate for the energy gained by the fluid particles due to diffusion, a cosmological scalar field term is added to the left hand side of the Einstein equations. This hypothesis promotes diffusion to a new mechanism for accelerated expansion in cosmology. It is shown that diffusion alters not only quantitatively, but also qualitatively the global dynamical properties of the standard cosmological models.     

Generic and nongeneric world models

Catastrophe theory methods are employed to obtain a new classification of those world models which can be presented in the form of gradient dynamical systems. Generic sets and structural stability of models in the potential space are strictly defined. It is shown that if a cosmological model is required to be Friedman and generic, it must be flat.     

Dynamical dimensional reduction

We propose to call a dynamical dimensional reduction effective if the corresponding dynamical system possesses a single attracting critical point representing expanding physical space-time and static internal space. We show that theBV × T ^D multidimensional cosmological model with a hydrodynamic energy-momentum tensor provides an example of effective dimensional reduction. We also study the dynamics of the multidimensional cosmological model of typeBI × T ^D with an energy-momentum tensor representing low temperature quantum effects, monopole contribution and the cosmological constant. It turns out that anisotropy and the cosmological constant are crucial for the process of dimensional reduction to be effective. We argue that this is the general property of homogeneous multidimensional cosmological models.     

Purely kinetic coupled gravity

Cosmic acceleration can be achieved not only with a sufficiently flat scalar field potential but through kinetic terms coupled to gravity. These derivative couplings impose a shift symmetry on the scalar field, aiding naturalness. We write the most general purely kinetic action not exceeding mass dimension 6 and obeying second order field equations. The result reduces to a simple form involving a coupling of the Einstein tensor with the kinetic term and can be interpreted as adding a new term to Galileon gravity in curved spacetime. We examine the cosmological implications of the effective dark energy and classify the dynamical attractor solutions, finding a quasistable loitering phase mimicking late time acceleration by a cosmological constant.     

Dynamical Vacuum in Quantum Cosmology

By regarding the vacuum as a perfect fluid with equation of state p = -, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom, following modern ideas that the cosmological term is a manifestation of the vacuum energy. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found, whose properties are studied. It is found that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.     

Spherical Solutions due to the Exterior Geometry of a Charged Weyl Black Hole

Firstly we derive peculiar spherical Weyl solutions, using a general spherically symmetric metric due to a massive charged object with definite mass and radius. Afterwards, we present new analytical solutions for relevant cosmological terms, which appear in the metrics. Connecting the metrics to a new geometric definition of a charged Black Hole, we numerically investigate the effective potentials of the total dynamical system, considering massive and massless test particles, moving on such Black Holes.     

Scalar–vector–tensor gravity from preferred reference frame effects

Using some suitable combinations of a dynamical unit time-like four-velocity of a preferred reference frame, Ricci tensor and covariant derivatives of the Brans–Dicke (BD) scalar field, we propose a new scalar–vector–tensor gravity model in which an Euclidean Jordan–Brans–Dicke (JBD) action is reduced to its Lorentzian version with no used complex coordinates. Thus it should be play an important role in the process of metric signature transition of a suitable dynamical curved space-time. In this work we follow the ideas proposed by Barbero et al. As an application of the model, we study a classical perfect fluid cosmological universe described in a flat Robertson–Walker background metric. Mathematical derivations of the equations predict a non-singular scale factor for the space-time in the both of dust and radiation dominated states where value of the Brans–Dicke parameter is fixed, but there is still an arbitrary parameter which should be determined by the boundary values of the cosmological system. Furthermore its classical cosmological vacuum solutions is obtained as a non-singular model with a fixed Brans–Dicke parameter. Although there is obtained a singular perfect fluid cosmological solution which may not be suitable, because in this case the Brans–Dicke parameter is not still fixed.     

Fractional Action Cosmology with Variable Order Parameter

Fractional action cosmology with variable order parameter was constructed in this paper. Starting from a fractional weighted action which generalizes the fractional actionlike variational approach, a large number of cosmological dynamical equations are obtained depending on the mathematical type of the fractional order parameter. Through this paper, we selected two independent types which result on a number of cosmological scenarios and we discussed their dynamical consequences. It was observed that the present fractional cosmological formalism holds a large family of solutions and offers new features not found in the standard formalism and in many fundamental research papers.     

Superpotentials and the Cohomogeneity One Einstein Equations

Using ideas from convex geometry, we prove a classification theorem, under suitable hypotheses, for superpotentials of the Hamiltonian form of the cohomogeneity one Ricci-flat equations. Some new superpotentials are also constructed and their associated first order systems analysed. The situation with a cosmological constant is briefly examined.The second author was partly supported by NSERC grant No. OPG0009421.     

Gravitational coupling and dynamical reduction of the cosmological constant

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner, a decaying mechanism is presented in which the conformal factor appears as a dynamical field and plays a key role to relax a large effective cosmological constant. Moreover, we argue that this model also provides a possible explanation for the coincidence problem.     

Spatially Homogeneous Bianchi Type-I Universes with Variable G and Λ

In this paper, we have studied the cosmological models of Bianchi type-I universes in a different basic form filled with bulk viscous fluid, in the presence of time-dependent gravitational as well as cosmological constants. A set of new exact cosmological solutions have been obtained in both full and truncated causal theories. These solutions are suitable for describing the evolution of the universe in its early stages. The physical and dynamical consequences have been discussed in detail.     

Quantifying self-organization with optimal predictors

Despite broad interest in self-organizing systems, there are few quantitative, experimentally applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we propose a new criterion, namely, an internally generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. We precisely define this complexity for spatially extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. This leads to a general method for predicting such systems and a simple algorithm for estimating statistical complexity. The results of applying this algorithm to a class of models of excitable media (cyclic cellular automata) strongly support our proposal.     

Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems

We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time) rather than in configuration space. To illustrate our general ideas, we analyze the one-dimensional (d = 1) Fredrickson-Andersen and East models. Dynamics of such dynamically constrained systems are shown to be isomorphic to the statics of ( d + 1)-dimensional dense mixtures of polydisperse noninterpenetrating domains. The domains coincide with arrested regions in trajectory space.     

General solutions for a cosmological Robertsonwalker metric in the Brans-Dicke theory

The general vacuum solutions of the Brans-Dicke theory in a cosmological Robertson-Walker-type metric are explicitly given. Several families of solutions have properties which essentially differ from the conventional Einstein theory. The geometry is not uniquely determined by the equations of motion, raising doubts about the “Machian” character of the Brans-Dicke theory. The role of the cosmological constant is emphasized, in agreement with modern ideas of fundamental particle interactions.