The dynamics of a universe dominated by a self-interacting nonminimally coupled scalar field are considered. The structure of the phase space and complete phase portraits are given. New dynamical behaviors include superinflation ($\dot{H}>0$), avoidance of big bang singularities through classical birth of the universe, and spontaneous entry into and exit from inflation. This model is promising for describing quintessence as a nonminimally coupled scalar field.Comment: 4 pages, 2 figure

A spatially flat FLRW universe (motivated by inflation) is studied; by a dimensional reduction of the dynamical equations of scalar field cosmology, it is demonstrated that a spatially flat universe cannot exhibit chaotic behaviour. The result holds when the source of gravity is a non-minimally coupled scalar field, for any self-interaction potential and for arbitrary values of the coupling constant with the Ricci curvature. The phase space of the dynamical system is studied, and regions inaccessible to the evolution are found. The topology of the forbidden regions, their dependence on the parameters, the fixed points and their stability character, and the asymptotic behaviour of the solutions are studied. New attractors are found, in addition to those known from the minimal coupling case, certain exact solutions are presented and the implications for inflation are discussed. The equation of state is not prescribed a priori , but rather is deduced self-consistently from the field equations.

Quasistationary states of long-range interacting systems have been studied at length over the last 15 years. It is known that the collisional terms of the Balescu-Lenard and Landau equations vanish for one-dimensional systems in homogeneous states, thus requiring a new kinetic equation with a proper dependence on the number of particles. Here we show that the scalings discussed in the literature are mainly due either to small size effects or the use of unsuitable variables to describe the dynamics. The scaling obtained from both simulations and theoretical considerations is proportional to the square of the number of particles, and a general form for the kinetic equation valid for the homogeneous regime is obtained. Numerical evidence is given for the Hamiltonian mean field and ring models, and a kinetic equation valid for the homogeneous state is obtained for the former system.

In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian Mean Field model and show that the life-time of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution.

Although the Vlasov equation is used as a good approximation for a sufficiently large N , Braun and Hepp have showed that the time evolution of the one particle distribution function of a N particle classical Hamiltonian system with long range interactions satisfies the Vlasov equation in the limit of infinite N . Here we rederive this result using a different approach allowing a discussion of the role of inter-particle correlations on the system dynamics. Otherwise for finite N collisional corrections must be introduced. This has allowed the a quite comprehensive study of the Quasi Stationary States (QSS) but many aspects of the physical interpretations of these states remain unclear. In this paper a proper definition of timescale for long time evolution is discussed and several numerical results are presented, for different values of N . Previous reports indicates that the lifetimes of the QSS scale as N 1.7 or even the system properties scales with exp(N ). However, preliminary results presented here shows indicates that time scale goes as N 2 for a different type of initial condition. We also discuss how the form of the inter-particle potential determines the convergence of the N -particle dynamics to the Vlasov equation. The results are obtained in the context of following models: the Hamiltonian Mean Field, the Self Gravitating Ring Model, and a 2-D Systems of Gravitating Particles. We have also provided information of the validity of the Vlasov equation for finite N , i. e. how the dynamics converges to the mean-field (Vlasov) description as N increases and how inter-particle correlations arise.