A. Figueiredo

Superinflation, quintessence, and nonsingular cosmologies

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 (

Boundedness of solutions and Lyapunov functions in quasi-polynomial systems

dot{H}>0

On the stability of a class of general non-linear systems

), 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.

[QPSI] A maple package for the determination of quasi-polynomial symmetries and invariants

Abstract In this Letter we establish sufficient conditions for the existence of a Lyapunov function for a large class of non-linear systems, the Quasi-Polynomial systems [Figueredo et al., J. Math. Phys. 39 (1998) 2929; Figueredo et al., Phys. A 262 (1999) 158; Brenig, Phys. Lett. A 133 (1988) 378] . We also present sufficient conditions such that the solutions are bounded and bounded away from zero componentwise.

Phase transitions in simplified models with long-range interactions

Abstract In a previous work (Phys. Lett. A 268 (2000) 335) the authors established sufficient conditions for the boundedness of solutions and stability of the interior fixed points for a class of general non-linear systems—the quasi-polynomial (QP) systems—and an algebraic method to analyse the problem. In this Letter we present an extension of our results based on a numeric approach which greatly enlarges the scope of applications of the method.

A no-chaos theorem for non-minimally coupled scalar field cosmology and a new cosmogenesis scenario

We present the QPSI (Quasi-Polynomial Symmetries and Invariants) MAPLE package for the systematic determination of quasi-polynomial symmetries, invariants and invariant tensor fields for dynamical systems. A brief survey of the theoretical results obtained by the authors used in the package is given.

Superinflation and quintessence in the presence of an extra field

We study the origin of phase transitions in several simplified models with long-range interactions. For the self-gravitating ring model, we are unable to observe a possible phase transition predicted by Nardini and Casetti [Phys. Rev. E 80, 060103R (2009).] from an energy landscape analysis. Instead we observe a sharp, although without any nonanalyticity, change from a core-halo to a core-only configuration in the spatial distribution functions for low energies. By introducing a different class of solvable simplified models without any critical points in the potential energy we show that a behavior similar to the thermodynamics of the ring model is obtained, with a first-order phase transition from an almost homogeneous high-energy phase to a clustered phase and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features for the simplified models and show that the first-order phase transition comes from the maximization of the entropy of the system as a function of energy and an order parameter, as previously discussed by Hahn and Kastner [Phys. Rev. E 72, 056134 (2005); Eur. Phys. J. B 50, 311 (2006)], which seems to be the main mechanism causing phase transitions in long-range interacting systems.

Nonequilibrium phase transitions and violent relaxation in the Hamiltonian mean-field model.

A general dynamical system approach to classical self-consistent scalar field cosmology is presented in the framework of spatially flat FLRW space–times, for arbitrary potentials and arbitrary non-minimal coupling. We show that these universes cannot undergo chaotic behaviors, thus suggesting a possible new role of inflation in cosmology. An unexpectedly involved topology of the phase-portrait of the cosmological dynamics is exhibited: Dynamically forbidden regions, playing a crucial dynamical role, appear. A new exact critical solution, a heteroclinic orbit, connects two de Sitter inflationary regimes. We suggest a novel intriguing semiclassical cosmogenesis scenario in which the quantized scalar field could tunnel through the classically forbidden region, from the Minkowski space–time towards the nearest classically allowed solution: The critical one.

Stability properties of nonlinear dynamical systems and evolutionary stable states

We discuss the implication of the introduction of an extra field to the dynamics of a scalar field conformally coupled to gravitation in a homogeneous isotropic spatially flat universe. We show that for some reasonable parameter values the dynamical effects are similar to those of our previous model with a single scalar field. Nevertheless, for other parameter values new dynamical effects are obtained.