Ricardo García-Salcedo

BORN–INFELD COSMOLOGIES

We present a model for an inhomogeneous and anisotropic early universe filled with a nonlinear electromagnetic field of Born–Infeld (BI) type. The effects of the BI field are compared with the linear case (Maxwell). Since the curvature invariants are well behaved then we conjecture that our model does not present an initial big bang singularity. The existence of the BI field modifies the curvature invariants at t=0 as well as sets bounds on the amplitude of the conformal metric function.

The conformal transformation’s controversy: what are we missing?

An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation’s issue is then revealed: these transformations relate complementary geometrical pictures of a same physical reality, so that, the question about which is the physical conformal frame, does not arise. In addition, arguments are given which point out that, unless a clear statement of what is understood by “equivalence of frames” is made, the issue is a semantic one. For definiteness, an intuitively “natural” statement of conformal equivalence is given, which is associated with conformal invariance of the field equations. Under this particular reading, equivalence can take place only if the metric is defined up to a conformal equivalence class. A concrete example of a conformal-invariant theory of gravity is then explored. Since Brans–Dicke theory is not conformally invariant, then the Jordan’s and Einstein’s frames of the theory are not equivalent. Otherwise, in view of the alternative approach proposed here, these frames represent complementary geometrical descriptions of a same phenomenon. The different points of view existing in the literature are critically scrutinized on the light of the new arguments.

No compelling cosmological models come out of magnetic universes which are based on nonlinear electrodynamics

Here we investigate the cosmic dynamics of Friedmann-Robertson-Walker universes – flat spatial sections – which are driven by nonlinear electrodynamics (NLED) Lagrangians. We pay special attention to the check of the sign of the square sound speed since, whenever the latter quantity is negative, the corresponding cosmological model is classically unstable against small perturbations of the background energy density. Besides, based on causality arguments, one has to require that the mentioned small perturbations of the background should propagate at most at the local speed of light. We also look for the occurrence of curvature singularities. Our results indicate that several cosmological models which are based in known NLED Lagrangians, either are plagued by curvature singularities of the sudden and/or big rip type, or are violently unstable against small perturbations of the cosmological background – due to negative sign of the square sound speed – or both. In addition, causality issues associated with superluminal propagation of the background perturbations may also arise.

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

Singularity-free Bianchi spaces with nonlinear electrodynamics

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

Introduction to the application of dynamical systems theory in the study of the dynamics of cosmological models of dark energy

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

Nonlinear electrodynamics in Bianchi spacetimes

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

Bulk viscous matter-dominated Universes: asymptotic properties

, 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.

QCD ghost dark energy cannot (even roughly) explain the main features of the accepted cosmological paradigm

In this paper we present an analysis to determine the existence of singularities in spatially homogeneous anisotropic universes filled with nonlinear electromagnetic radiation. These spaces are conformal to Bianchi spaces admitting a three parameter group of motions G3. For these models we study geodesic completeness. It is shown that with nonlinear electromagnetic field some of the Bianchi spaces are geodesically complete (G3VIII). The analysis of the Raychaudhuri equation reveals that the BI field is responsible for the absence of singularity. When certain topology is assumed, Bianchi G3IX may present geodesics that are imprisoned. In the linear limit (Maxwell field) the spacetimes are singular and they do not admit a cosmological interpretation in all the range of the time coordinate.

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

The theory of dynamical systems is a very complex subject that has produced several surprises in the recent past in connection with the theory of chaos and fractals. The application of the tools of dynamical systems in cosmological settings is less known, in spite of the number of published scientific papers on this subject. In this paper, a mostly pedagogical introduction to the cosmological application of the basic tools of dynamical systems theory is presented. It is shown that, in spite of their amazing simplicity, these tools allow us to extract essential information on the asymptotic dynamics of a wide variety of cosmological models. The power of these tools is illustrated within the context of the so-called ?-cold dark matter (?CDM) and scalar field models of dark energy. This paper is suitable for teachers, undergraduate students, and postgraduate students in the disciplines of physics and mathematics.