# Genly Leon - Valparaiso University, Catolica

## Contact Details

NameGenly Leon |
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AffiliationValparaiso University, Catolica |
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CityValparaiso |
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CountryChile |
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## Pubs By Year |
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## Pub CategoriesGeneral Relativity and Quantum Cosmology (34) High Energy Physics - Theory (25) Cosmology and Nongalactic Astrophysics (21) Astrophysics (6) High Energy Physics - Phenomenology (3) Mathematics - Mathematical Physics (2) Mathematical Physics (2) Mathematics - Dynamical Systems (2) |

## Publications Authored By Genly Leon

Recently a cubic Galileon cosmological model was derived by the assumption that the field equations are invariant under the action of point transformations. The cubic Galileon model admits a second conservation law which means that the field equations form an integrable system. The analysis of the critical points for this integrable model is the main subject of this work. Read More

A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the Friedmann-Lema\^itre-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Due to the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability. Read More

We investigate all spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1+1+2 formalism and introducing suitable normalized variables involving the Gaussian curvature, we were able to reformulate the field equations as first order differential equations. In the case of a massless canonical scalar field we recovered all known black hole results, such as the Fisher solution, and we found that apart from the Schwarzschild solution all other solutions are naked singularities. Read More

**Affiliations:**

^{1}Dalhousie U., Math. Dept.,

^{2}Valparaiso U., Catolica,

^{3}Chile Austral U., Valdivia

We investigate Kantowski-Sachs models in Einstein-{\ae}ther theory with a perfect fluid source using the singularity analysis to prove the integrability of the field equations and dynamical system tools to study the evolution. We find an inflationary source at early times, and an inflationary sink at late times, for a wide region in the parameter space. The results by A. Read More

In this paper we apply the tools of the dynamical systems theory in order to uncover the whole asymptotic structure of the vacuum interactions of a galileon model with a cubic derivative interaction term. It is shown that, contrary to what occurs in the presence of background matter, the galileon interactions of vacuum appreciably modify the late-time cosmic dynamics. In particular, a local late-time attractor representing phantom behavior arises which is inevitably associated with a big rip singularity. Read More

**Affiliations:**

^{1}Dalhousie U., Math. Dept.,

^{2}Valparaiso U., Catolica,

^{3}Potsdam, Max Planck Inst.,

^{4}Dalhousie U., Math. Dept.

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. Read More

**Affiliations:**

^{1}Biobio U.,

^{2}Valparaiso U., Catolica,

^{3}Tarapaca U.

We investigate a Jordan-Brans-Dicke (JBD) scalar field, $\Phi$, with
power-law potential in the presence of a second scalar field, $\phi$, with an
exponential potential, in both the Jordan and the Einstein frames. We present
the relation of our model with the induced gravity model with power-law
potential and the integrability of this kind of models is discussed when the
quintessence field $\phi$ is massless, and has a small velocity. We prove that
in JBD theory, the de Sitter solution is not a natural attractor but an
intermediate accelerated solution of the form $a(t)\simeq e^{\alpha_1
t^{p_1}}$, as $t\rightarrow \infty$ where $\alpha_1>0$ and $0

**Affiliations:**

^{1}Valparaiso U., Catolica,

^{2}Natl. Tech. U., Athens & Valparaiso U., Catolica

We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a way that the algebra of constraints and local physics remain unchanged. Nevertheless, at cosmological scales these new terms can have significant effects that can alter the universe evolution, both at early and late times, and the freedom in the choice of the involved modification function makes the scenario able to produce a huge class of cosmological behaviors. For basic ansatzes of modification, we perform a detailed dynamical analysis, extracting the stable late-time solutions. Read More

**Affiliations:**

^{1}Valparaiso U., Catolica,

^{2}Natl. Tech. U., Athens & Valparaiso U., Catolica

**Category:**General Relativity and Quantum Cosmology

We investigate the cosmological behavior of mimetic F(R) gravity. This scenario is the F(R) extension of usual mimetic gravity classes, which are based on re-parametrizations of the metric using new, but not propagating, degrees of freedom, that can lead to a wider family of solutions. Performing a detailed dynamical analysis for exponential, power-law, and arbitrary F(R) forms, we extracted the corresponding critical points. Read More

The problem of dark energy can be roughly stated as the proposition and validation of a cosmological model that can explain the phenomenon of the accelerated expansion of the Universe. This problem is an open discussion topic in modern physics. One of the most common approaches is that of the "Dark Energy" (DE), a matter component still unknown, with repulsive character (to explain the accelerated expansion), which fills about 2/3 of the total content of the Universe. Read More

In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and useful tools from the qualitative theory of dynamical systems. Read More

**Affiliations:**

^{1}Valparaiso U., Catolica,

^{2}Valparaiso U., Catolica,

^{3}Valparaiso U., Catolica,

^{4}Tarapaca U.

We study higher derivative terms associated with scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired by the Pais-Uhlenbeck oscillator, given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. Read More

**Affiliations:**

^{1}Havana, Central de Las Villas U.,

^{2}Valparaiso U., Catolica

Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling functions are considered. Mild assumptions under such functions (differentiable class, number of singular points, asymptotes, etc) are introduced in a straightforward manner in order to characterize the asymptotic structure on a phase space. Read More

**Affiliations:**

^{1}Aegean U.,

^{2}Valparaiso U., Catolica,

^{3}Natl. Tech. U., Athens & Valparaiso U., Catolica

The $f(T,T_G)$ class of gravitational modification, based on the quadratic torsion scalar $T$, as well as on the new quartic torsion scalar $T_G$ which is the teleparallel equivalent of the Gauss-Bonnet term, is a novel theory, different from both $f(T)$ and $f(R,G)$ ones. We perform a detailed dynamical analysis of a spatially flat universe governed by the simplest non-trivial model of $f(T,T_G)$ gravity which does not introduce a new mass scale. We find that the universe can result in dark-energy dominated, quintessence-like, cosmological-constant-like or phantom-like solutions, according to the parameter choices. Read More

We construct general anisotropic cosmological scenarios governed by an $f(R)=R^n$ gravitational sector. Focusing then on some specific geometries, and modelling the matter content as a perfect fluid, we perform a phase-space analysis. We analyze the possibility of accelerating expansion at late times, and additionally, we determine conditions for the parameter $n$ for the existence of phantom behavior, contracting solutions as well as of cyclic cosmology. Read More

**Affiliations:**

^{1}Valparaiso U., Catolica,

^{2}Cienfuegos U., Cuba

In this paper we investigate, from the dynamical systems perspective, the evolution of a Kantowski-Sachs metric in a generic class of $f(R)$ models. We present conditions (i. e. Read More

**Affiliations:**

^{1}Havana, Central de Las Villas U.,

^{2}Valparaiso U., Catolica,

^{3}Natl. Tech. U., Athens & Valparaiso U., Catolica

We perform a detailed dynamical analysis of anisotropic scalar-field cosmologies, and in particular of the most significant Kantowski-Sachs, Locally Rotationally Symmetric (LRS) Bianchi I and LRS Bianchi III cases. We follow the new and powerful method of $f$-devisers, which allows us to perform the whole analysis for a wide range of potentials. Thus, one can just substitute the specific potential form in the final results and obtain the corresponding behavior, without the need of new calculations. Read More

In this paper we consider a cosmological model whose main components are a scalar field and a generalized Chaplygin gas. We obtain an exact solution for a flat arbitrary potential. This solution have the right dust limit when the Chaplygin parameter $A\rightarrow 0$. Read More

**Affiliations:**

^{1}Valparaiso U., Catolica,

^{2}Valparaiso U., Catolica,

^{3}Natl. Tech. U., Athens & Valparaiso U., Catolica

We perform a detailed dynamical analysis of various cosmological scenarios in extended (varying-mass) nonlinear massive gravity. Due to the enhanced freedom in choosing the involved free functions, this cosmological paradigm allows for a huge variety of solutions that can attract the universe at late times, comparing to scalar-field cosmology or usual nonlinear massive gravity. Amongst others, it accepts quintessence, phantom, or cosmological-constant-like late-time solutions, which moreover can alleviate the coincidence problem. Read More

**Affiliations:**

^{1}Camaguey U.,

^{2}Havana, Central de Las Villas U.,

^{3}Valparaiso U., Catolica,

^{4}Valparaiso U., Catolica & Guanajuato U.

In this work we present a phase space analysis of a quintessence field and a perfect fluid trapped in a Randall-Sundrum's Braneworld of type 2. We consider a homogeneous but anisotropic Bianchi I brane geometry. Moreover, we consider the effect of the projection of the five dimensional Weyl tensor onto the three-brane in the form of a negative Dark Radiation term. Read More

**Affiliations:**

^{1}Havana, Central de Las Villas U. & Valparaiso U., Catolica,

^{2}Natl. Tech. U.Athens & Baylor U.

We perform a detailed dynamical analysis of generalized Galileon cosmology, incorporating also the requirements of ghost and instabilities absence. We find that there are not any new stable late-time solutions apart from those of standard quintessence. Furthermore, depending on the model parameters the Galileons may survive at late times or they may completely disappear by the dynamics, however the corresponding observables are always independent of the Galileon terms, determined only by the usual action terms. Read More

We investigate the phase-space structure of the quintom dark energy paradigm in the framework of spatially flat and homogeneous universe. Considering arbitrary decoupled potentials, we find certain general conditions under which the phantom dominated solution is late time attractor, generalizing previous results found for the case of exponential potential. Center Manifold Theory is employed to obtain sufficient conditions for the instability of de Sitter solution either with phantom or quintessence potential dominance. Read More

**Affiliations:**

^{1}CUPT, Chongqing,

^{2}Natl. Tech. U., Athens and Baylor U.,

^{3}Havana, Central de Las Villas U.

We perform a detailed dynamical analysis of the teleparallel dark energy scenario, which is based on the teleparallel equivalent of General Relativity, in which one adds a canonical scalar field, allowing also for a nonminimal coupling with gravity. We find that the universe can result in the quintessence-like, dark-energy-dominated solution, or to the stiff dark-energy late-time attractor, similarly to standard quintessence. However, teleparallel dark energy possesses an additional late-time solution, in which dark energy behaves like a cosmological constant, independently of the specific values of the model parameters. Read More

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 2. We consider an homogeneous but anisotropic Bianchi I (BI) brane filled also with a perfect fluid. We also consider the effect of the projection of the five-dimensional Weyl tensor onto the three-brane in the form of a positive Dark Radiation term. Read More

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. Read More

We investigate the phase-space of a flat FRW universe including both a scalar field, $\phi,$ coupled to matter, and radiation. The model is inspired in scalar-tensor theories of gravity, and thus, related with $F(R)$ theories through conformal transformation. The aim of the chapter is to extent several results to the more realistic situation when radiation is included in the cosmic budget particularly for studying the early time dynamics. Read More

We construct general anisotropic cosmological scenarios governed by an $f(R)$
gravitational sector. Focusing then on Kantowski-Sachs geometries in the case
of $R^n$-gravity, and modelling the matter content as a perfect fluid, we
perform a detailed phase-space analysis. We find that at late times the
universe can result to a state of accelerating expansion, and additionally, for
a particular $n$-range ($2

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. Read More

We perform a detailed phase-space analysis of Horava-Lifshitz cosmology, with and without the detailed-balance condition. Under detailed-balance we find that the universe can reach a bouncing-oscillatory state at late times, in which dark-energy, behaving as a simple cosmological constant, is dominant. In the case where the detailed-balance condition is relaxed, we find that the universe reaches an eternally expanding, dark-energy-dominated solution, with the oscillatory state preserving also a small probability. Read More

We investigate several varying-mass dark-matter particle models in the framework of phantom cosmology. We examine whether there exist late-time cosmological solutions, corresponding to an accelerating universe and possessing dark energy and dark matter densities of the same order. Imposing exponential or power-law potentials and exponential or power-law mass dependence, we conclude that the coincidence problem cannot be solved or even alleviated. Read More

We apply dynamical systems techniques to investigate cosmological models inspired in scalar-tensor theories written in the Einstein frame. We prove that if the potential and the coupling function are sufficiently smooth functions, the scalar field almost always diverges into the past. The dynamics of two important invariant sets is investigated in some detail. Read More

In the previous paper \cite{Lazkoz:2006pa} was investigated the phase space of quintom cosmologies for a class of exponential potentials. This study suggests that the past asymptotic dynamics of such a model can be approximated by the dynamics near a hyperbola of critical points. In this paper we obtain a normal form expansion near a fixed point located on this equilibrium set. Read More

We explore quintessence models of dark energy which exhibit non-minimal coupling between the dark matter and the dark energy components of the cosmic fluid. The kind of coupling chosen is inspired in scalar-tensor theories of gravity. We impose a suitable dynamics of the expansion allowing to derive exact Friedmann-Robertson-Walker solutions once the coupling function is given as input. Read More

In this paper we investigate quintom cosmologies with arbitrary potentials from the dynamical systems perspective. The dynamical systems analysis is complete in the sense that it includes the asymptotic regime where both scalar fields diverge, which proves to be particularly relevant in connection with the existence of tracking phases. The results of the present study indicate that the existence of phantom attractors is not generic: for quintom models there may exist either de Sitter attractors associated with the saddle points of the potential, or tracking attractors in the asymptotic regime where the scalar fields diverge. Read More

In this paper we investigate the evolution of a class of cosmologies fuelled by quintom dark energy and dark matter. Quintom dark energy is a hybrid of quintessence and phantom which involves the participation of two reals scalar fields playing the roles of those two types of dark energy. In that framework we examine from a dynamical systems perspective the possibility that those fields are coupled among them by considering an exponential potential with an interesting functional dependence similar but not identical to others studied before. Read More

In this paper we analyze the asymptotic behavior of Cardassian cosmological models filled with a perfect fluid and a scalar field with an exponential potential. Cardassian cosmologies arise from modifications of the Friedmann equation, and among the different proposals within that framework we will choose those of the form $3H^2-\rho\propto \rho^n$ with $n<1$. We construct two three dimensional dynamical systems arising from the evolution equations, respectively adapted for studying the high and low energy limits. Read More

We explore quintessence models of dark energy which exhibit non-minimal coupling between the dark matter and the dark energy components of the cosmic fluid. The kind of coupling chosen is inspired in scalar-tensor theories of gravity. We impose a suitable dynamics of the expansion allowing to derive exact Friedmann-Robertson-Walker solutions once the coupling function is given as input. Read More

Models of the universe with arbitrary (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 in scalar-tensor theories of gravity is considered. No specific model for the phantom fluid is assumed. Read More