arXiv subjects

Yoelsy Leyva

Publications and source records attributed to Yoelsy Leyva.

25 records · Page 2Linked to original sources

arXiv2012

Phase space analysis of quintessence fields trapped in a Randall-Sundrum braneworld: a refined study

In this paper we investigate, from the dynamical systems perspective, the evolution of an scalar field with arbitrary potential trapped in a Randall-Sundrum's Braneworld of type II. We consider an homogeneous and isotropic Friedmann-Robertson-Walker (FRW) brane filled also with a perfect fluid. Center Manifold Theory is employed to obtain sufficient conditions for the asymptotic stability of de Sitter solution. We obtain conditions on the potential for the stability of scaling solutions as well for the stability of the scalar-field dominated solution. We prove the there are not late time attractors with 5D-modifications (they are saddle-like). This fact correlates with a transient primordial inflation. In the particular case of a scalar field with potential $V=V_{0}e^{-χϕ}+Λ$ we prove that for $χ<0$ the de Sitter solution is asymptotically stable. However, for $χ>0$ the de Sitter solution is unstable (of saddle type).

gr-qc↗

arXiv2010

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

We apply the dynamical systems tools to study the asymptotic properties of a cosmological model based on a non-linear modification of General Relativity in which the standard Einstein-Hilbert action is replaced by one of Dirac-Born-Infeld type. It is shown that the dynamics of this model is extremely rich: there are found equilibrium points in the phase space that can be associated with matter-dominated, matter-curvature scaling, de Sitter, and even phantom-like solutions. Depending on the value of the overall parameters the dynamics in phase space can show multi-attractor structure into the future (multiple future attractors may co-exist). This is a consequence of bifurcations in control parameter space, showing strong dependence of the model's dynamical properties on the free parameters. Contrary to what is expected from non-linear modifications of general relativity of this kind, removal of the initial spacetime singularity is not a generic feature of the corresponding cosmological model. Instead, the starting point of the cosmic dynamics -- the past attractor in the phase space -- is a state of infinitely large value of the Hubble rate squared, usually associated with the big bang singularity.

gr-qc↗

arXiv2009

Falsifying Field-based Dark Energy Models

We survey the application of specific tools to distinguish amongst the wide variety of dark energy models that are nowadays under investigation. The first class of tools is more mathematical in character: the application of the theory of dynamical systems to select the better behaved models, with appropriate attractors in the past and future. The second class of tools is rather physical: the use of astrophysical observations to crack the degeneracy of classes of dark energy models. In this last case the observations related with structure formation are emphasized both in the linear and non-linear regimes. We exemplify several studies based on our research, such as quintom and quinstant dark energy ones. Quintom dark energy paradigm is a hybrid construction of quintessence and phantom fields, which does not suffer from fine-tuning problems associated to phantom field and additionally it preserves the scaling behavior of quintessence. Quintom dark energy is motivated on theoretical grounds as an explanation for the crossing of the phantom divide, i.e. the smooth crossing of the dark energy state equation parameter below the value -1. On the other hand, quinstant dark energy is considered to be formed by quintessence and a negative cosmological constant, the inclusion of this later component allows for a viable mechanism to halt acceleration. We comment that the quinstant dark energy scenario gives good predictions for structure formation in the linear regime, but fails to do that in the non-linear one, for redshifts larger than one. We comment that there might still be some degree of arbitrariness in the selection of the best dark energy models.

gr-qc↗

arXiv2009

Dynamics of a Self-interacting Scalar Field Trapped in the Braneworld for a Wide Variety of Self-interaction Potentials

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 (RS) and on Dvali-Gabadadze-Porrati (DGP) braneworld models exclusively. These models are complementary to each other: while the RS brane produces ultra-violet (UV) corrections to general relativity, the DGP braneworld modifies Einstein's theory at large scales, i. e., produces infra-red (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 behaviour.

gr-qc↗

arXiv2009

A Note on de Sitter Embedding of $f(R)$ Theories

The consequences of the constraints which de Sitter embedding of $f(R)$ theories imposes on the Lagrangian's parameters, are investigated within the metric formalism. It is shown, in particular, that several common $f(R)$ Lagrangians do not actually admit such an embedding. Otherwise, asymptotic matching of local solutions of the corresponding models with background (maximally symmetric) spaces of constant curvature is either unstable or, anti-de Sitter embedding is the only stable embedding. Additional arguments are given in favour of a previous claim that a class of $f(R)$ models comprising both positive and negative powers of $R$ (two different mass scales), could be a nice scenario where to address, in a united picture, both early-time inflation and late-time accelerated expansion of the universe. The approach undertaken here is used, also, to check ghost-freedom of a Dirac-Born-Infeld modification of general relativity previously studied in the bibliography.

gr-qc↗

arXiv2007

Evolution of density perturbations in double exponential quintessence models

In this work we investigate the evolution of matter density perturbations for quintessence models with a self-interaction potential that is a combination of exponentials. One of the models is based on the Einstein theory of gravity, while the other is based on the Brans-Dicke scalar tensor theory. We constrain the parameter space of the models using the determinations for the growth rate of perturbations derived from data of the 2-degree Field Galaxy Redshift Survey.

astro-ph↗

arXiv2003

Exact Scaling Solutions in Normal and Brans-Dicke Models of Dark Energy

A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is explored in order to derive exact cosmological, attractor-like solutions, both in Einstein's theory and in Brans-Dicke gravity with two fluids: a background fluid of ordinary matter, together with a self-interacting scalar field accounting for the dark energy in the universe. A priori assumptions about the functional form of the self-interaction potential or about the scale factor behavior are not necessary. These are obtained as outputs of the assumed relationship between the Hubble parameter and the time derivative of the scalar field. A parametric class of scaling quintessence models given by a self-interaction potential of a peculiar form: a combination of exponentials with dependence on the barotropic index of the background fluid, arises. Both normal quintessence described by a self-interacting scalar field minimally coupled to gravity and Brans-Dicke quintessence given by a non-minimally coupled scalar field are then analyzed and the relevance of these models for the description of the cosmic evolution are discussed in some detail. The stability of these solutions is also briefly commented on.

gr-qc↗