Tame Gonzalez

Interacting phantom energy and avoidance of the big rip singularity

Models of the universe with additional (non-gravitational) interaction between the components of the cosmic fluid—the phantom energy and the background—are investigated. A general form of the interaction that is inspired by scalar–tensor theories of gravity is considered. No specific model for the phantom fluid is assumed. We concentrate our investigation on solutions which are free of the coincidence problem. Solutions with constant and dynamical equation-of-state parameters are studied separately. In the last case the model allows for smooth transition from dust in the past into phantom in the future. We found a wide region in the parameter space where the solutions are also free of big rip singularity. Physical arguments, together with arguments based on the analysis of the observational evidence, suggest that phantom models without the big rip singularity might be preferred by nature.

Dynamics of quintessence models of dark energy with exponential coupling to dark matter

We explore quintessence models of dark energy which exhibit non-minimal coupling between the dark matter and dark energy components of the cosmic fluid. The kind of coupling chosen is inspired by scalar–tensor theories of gravity. We impose a suitable dynamics of the expansion allowing us to derive exact Friedmann–Robertson–Walker solutions once the coupling function is given as input. Self-interaction potentials of single and double exponential types emerge as a result of our choice of the coupling function. The stability and existence of the solutions are discussed in some detail. Although, in general, models with appropriate interaction between the components of the cosmic mixture are useful for handling the coincidence problem, in the present study this problem cannot be avoided due to the choice of solution generating ansatz.

A model of the universe including dark energy accounted for by both a quintessence field and a (negative) cosmological constant

In this work we explore a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field (with a double exponential self-interaction potential) and a cosmological constant. For a given region of the parameter space, our results confirm the possibility of a collapsing universe, which is necessary for an adequate definition of both perturbative quantum field and string theories. We have also reproduced the measurements of modulus distance from supernovae with good accuracy.

A study of tachyon dynamics for broad classes of potentials

We investigate in detail the asymptotic properties of tachyon cosmology for a broad class of self-interaction potentials. The present approach relies in an appropriate re-definition of the tachyon field, which, in conjunction with a method formerly applied in the bibliography in a different context, allows to generalize the dynamical systems study of tachyon cosmology to a wider class of self-interaction potentials beyond the (inverse) square-law one. It is revealed that independent of the functional form of the potential, the matter-dominated solution and the ultra-relativistic (also matter-dominated) solution, are always associated with equilibrium points in the phase space of the tachyon models. The latter is always the past attractor, while the former is a saddle critical point. For inverse power-law potentials

Dynamics of a self-interacting scalar field trapped in the braneworld for a wide variety of self-interaction potentials

V\propto\phi^{-2\lambda}

Self-interacting scalar field trapped in a Randall-Sundrum braneworld: The dynamical systems perspective

the late-time attractor is always the de Sitter solution, while for sinh-like potentials

Exact scaling solutions in normal and Brans–Dicke models of dark energy

V\propto\sinh^{-\alpha}(\lambda\phi)

Randall–Sundrum brane cosmology: modification of late-time cosmic dynamics by exotic matter

, depending on the region of parameter space, the late-time attractor can be either the inflationary tachyon-dominated solution or the matter-scaling (also inflationary) phase. In general, for most part of known quintessential potentials, the late-time dynamics will be associated either with de Sitter inflation, or with matter-scaling, or with scalar field-dominated solutions.

Asymptotic Properties of a Supposedly Regular (Dirac-Born-Infeld) Modification of General Relativity.

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped in the braneworld, for a wide variety of self-interaction potentials. We focus on Randall-Sundrum and on Dvali-Gabadadze-Porrati braneworld models exclusively. These models are complementary to each other: while the Randall-Sundrum brane produces UV) corrections to general relativity, the Dvali-Gabadadze-Porrati braneworld modifies Einsteins theory at large scales, i e., produces IR modifications of general relativity. This study of the asymptotic properties of both braneworld models, shows - in the phase space - the way the dynamics of a scalar field trapped in the brane departs from standard general relativity behavior.

Evolution of density perturbations in double exponential quintessence models

Abstract We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a Randall–Sundrum brane. The simplest kinds of self-interaction potentials are investigated: (a) constant potential, and (b) exponential potential. It is shown that the dynamics of the Randall–Sundrum model significantly differs from the standard four-dimensional behavior at early times: in all cases of interest the (singular) empty universe is the past attractor for every trajectory in phase space, meanwhile the kinetic energy-dominated solution is always a saddle critical point. The late-time dynamics is not affected by the brane effects.