# Genly LeonUniversidad Católica del Norte (Chile) · Department of Mathematics

Genly Leon

Ph. D. in Mathematics

Teaching and Research.

## About

162

Publications

9,769

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2,540

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Citations since 2016

Introduction

I study equations of the gravitational field in Einstein's general theory of relativity and modifications such as tenso-scalar theories, f(R) theories, theories with high derivatives, etc. I am interested in obtaining exact solutions of differential systems and the qualitative analysis of dynamical systems. For these studies I use physical-mathematical tools, dynamical systems theory, averaging theory and numerical methods which permit a detailed mathematical description of different models.

Additional affiliations

April 2017 - present

## Publications

Publications (162)

Fractional cosmology modifies the standard derivative to Caputo’s fractional derivative of order μ, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on μ and the age of the Universe tU. We estimate stringent constraints on μ using cosmic chronometers, Type Ia supernovae,...

In the present article, we show that a simple modification to the Einstein-Hilbert action can explain the possibility of mutual interaction between the cosmic fluids. That is achieved considering the Weyl Integrable Spacetime in the background of a nonflat Friedmann-Lemaître-Robertson-Walker geometry for the universe. We perform the dynamical syste...

We investigate exact solutions and the asymptotic dynamics for the Friedmann–Lemaître–Robertson–Walker universe with nonzero spatial curvature in the fourth‐order modified teleparallel gravitational theory known as f(T,B)$$ f\left(T,B\right) $$ theory. We show that the field equations admit a minisuperspace description, and they can reproduce any e...

We address the important issue of isotropisation of a pre-bounce contracting phase in f ( R ) gravity, which would be relevant to constructing any viable nonsingular bouncing scenario in f ( R ) gravity. The main motivation behind this work is to investigate whether the f ( R ) gravity, by itself, can isotropise a contracting universe starting init...

The Lie symmetry analysis for the study of a 1+n fourth-order Schrödinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed classification for the scalar field potential function where non-trivial Lie symmetries exist and simplify the Schrödinger equa...

We study the asymptotic dynamics of f(T, B)-theory in an anisotropic Bianchi III background geometry. We show that an attractor always exists for the field equations, which depends on a free parameter provided by the specific f(T, B) functional form. The attractor is an accelerated spatially flat FLRW or non-accelerated LRS Bianchi III geometry. Co...

We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to understand the evolution of solutions for various initial conditions as also to investigate the existence of a...

We consider a cosmological model consisting of two scalar fields defined in the hyperbolic plane known as hyperbolic inflation. For the background space, we consider a homogeneous and isotropic spacetime with nonzero curvature. We study the asymptotic behaviour of solutions and search for attractors in the expanding regime. We prove that two hyperb...

We present a unified description of the matter and dark energy epochs using a class of scalar-torsion theories. We provide a Hamiltonian description, and by applying Noether’s theorem and requiring the field equations to admit linear-in-momentum conservation laws, we obtain two specific classes of scalar-field potentials. First, we extract analytic...

We address the important issue of isotropisation of a pre-bounce contracting phase in f (R) gravity, which would be relevant to construct any viable nonsingular bouncing scenario in f (R) gravity. The main motivation behind this work is to investigate whether the f (R) gravity, by itself, can isotropise a contracting universe starting initially wit...

We study the asymptotic dynamics of $f(T, B)$-theory in an anisotropic Bianchi III background geometry. We show that an attractor always exists for the field equations, which depends on a free parameter provided by the specific $f(T, B)$ functional form. The attractor is an accelerated spatially flat FLRW or non-accelerated LRS Bianchi III geometry...

In the context of the modified teleparallel $f(T, B)$-theory of gravity, we consider a homogeneous and anisotropic background geometry described by the Kantowski-Sachs line element. We derive the field equations and investigate the existence of exact solutions. Furthermore, the evolution of the trajectories for the field equations is studied by der...

Fractional cosmology has emerged recently, based on the formalism of fractional calculus, which modifies the standard derivative to one fractional derivative of order $\alpha$. In this mathematical framework, the Friedmann equations are modified with an additional term, and the standard evolution of the cosmic species densities depends on the fract...

In the context of the modified teleparallel f(T, B) theory of gravity, we consider a homogeneous and anisotropic background geometry described by the Kantowski–Sachs line element. We derive the field equations and investigate the existence of exact solutions. Furthermore, the evolution of the trajectories for the field equations is studied by deriv...

We investigate the inflation driven by a non-linear electromagnetic field based on a NLED lagrangian density ${\cal L}_{nled} = - {\cal F} f \left( {\cal F} \right)$, where $f \left( {\cal F}\right)$ is a generalized functional depending on ${\cal F}$. We first formulate an $f$-NLED cosmological model with a more general functional $f \left( {\cal...

In the present article, we show that a simple modification to the Einstein-Hilbert action can explain the possibility of mutual interaction between the cosmic fluids. That is achieved considering the Weyl Integrable Spacetime in the background of a nonflat Friedmann-Lemna\^{i}tre-Robertson-Walker geometry for the universe. We show that widely-known...

Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann-Lemaître-Robertson-Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered. Asymptotic methods and averaging theory are used to obtain relevant information about the solution space. In this a...

The Lie symmetry analysis for the study of a $1+n~$fourth-order Schr\"{o}dinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed classification for the scalar field potential function where non-trivial Lie symmetries exist and simplify the Schr\"{o}d...

We revise recent results on the classification of the generalized three-dimensional Hamiltonian Ermakov system. We show that a statement published recently is incorrect, while the solution for the classification problem was incomplete. We present the correct classification for the three-dimensional system by using results which related the backgrou...

We revise recent results on the classification of the generalized three‐dimensional Hamiltonian Ermakov system. We show that a statement published recently is incorrect, while the solution for the classification problem was incomplete. We present the correct classification for the three‐dimensional system by using results which related the backgrou...

We investigate the integrability properties and existence of analytic solutions in $f\left( R\right) $-cosmology by using the singularity analysis. Specifically, for some power-law $f\left( R\right) $-theories of special interest we apply the ARS algorithm to prove if the field equations possess the Painlev\'{e} property. Constraints for the free p...

We shall present a complete (compactified) dynamical systems analysis of the Quintom model comprised of an interacting quintessence scalar field and a phantom scalar field. We find that there is a range for the model parameters $\kappa, \lambda$ such that there are expanding Quintom cosmologies that undergo two inflationary periods, and that this b...

We present a unified description of the matter and dark energy epochs, using a class of scalar-torsion theories. We provide a Hamiltonian description, and by applying Noether's theorem and by requiring the field equations to admit linear-in-momentum conservation laws we obtain two specific classes of scalar-field potentials. We extract analytic sol...

We study the scenario of Kanadiakis horizon entropy cosmology which arises from the application of the gravity-thermodynamics conjecture using the Kaniadakis modified entropy. The resulting modified Friedmann equations contain extra terms that constitute an effective dark energy sector. We use data from Cosmic chronometers, Supernova Type Ia, HII g...

We consider a cosmological model consisting of two scalar fields defined in the hyperbolic plane known as hyperbolic inflation. For the background space we consider a homogeneous and isotropic spacetime with nonzero curvature. We study the asymptotic behaviour of the dynamics and we search for attractors in the expanding regime. We prove that the h...

The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in R4. In this study, we investigate the behavior of trajectories in the presence of cosmological constant. It has been shown that the Szekeres system is a Hamiltonian dynamical system. It admits at least two conserva...

We consider a spatially flat Friedmann-Lemaître-Robertson-Walker background space with an ideal gas and a multifield Lagrangian consisting of two minimally coupled scalar fields which evolve in a field space of constant curvature. For this cosmological model we classify the potential function for the scalar fields such that variational point symmet...

We investigate Kaniadakis-holographic dark energy by confronting it with observations. We perform a Markov Chain Monte Carlo analysis using cosmic chronometers, supernovae type Ia, and Baryon Acoustic Oscillations data. Concerning the Kaniadakis parameter, we find that it is constrained around zero, namely around the value in which Kaniadakis entro...

We study the existence of exact solutions and the asymptotic dynamics for the cosmological scenario of a Friedmann--Lema\^{\i}tre--Robertson--Walker universe with nonzero spatial curvature in the fourth-order modified teleparallel gravitational theory, known as $f\left( T, B\right) $ theory. We show that the field equations admit a minisuperspace d...

We consider a modification of the Brans-Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans-Dicke scalar field is modified such that the equation of motion for the scalar field be modified according to the quadratic Generalized Uncertainty P...

We perform a detailed analysis of the asymptotic behavior of a multi-field cosmological model with phantom terms. Specifically, we consider the Chiral-Phantom model consisting of two scalar fields with a mixed kinetic term, where one scalar field has negative kinetic energy, that is, it has phantom properties. We show that the Hubble function can c...

We study the scenario of Kanadiakis horizon entropy cosmology which arises from the application of the gravity-thermodynamics conjecture using the Kaniadakis modified entropy. The resulting modified Friedmann equations contain extra terms that constitute an effective dark energy sector. We use data from Cosmic chronometers, Supernova Type Ia, HII g...

In this work, we use an observational approach and dynamical system analysis to study the cosmological model recently proposed by Saridakis (2020), which is based on the modification of the entropy-area black hole relation proposed by Barrow (2020). The Friedmann equations governing the dynamics of the Universe under this entropy modification can b...

In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields ϕ1 and ϕ2 interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless time variable, the resulting dynamical system is studied. The main difficulties arising in the standard dynamical systems...

We propose an Einstein-æther scalar–tensor cosmological model. In particular, in the scalar–tensor Action Integral, we introduce the æther field with æther coefficients to be functions of the scalar field. This cosmological model extends previous studies on Lorentz-violating theories. For a spatially flat Friedmann–Lemaître–Robertson–Walker backgro...

We investigate Kaniadakis-holographic dark energy by confronting it with observations. We perform a Markov Chain Monte Carlo analysis using cosmic chronometers, supernovae type Ia, and Baryon Acoustic Oscillations data. Concerning the Kaniadakis parameter, we find that it is constrained around zero, namely around the value in which Kaniadakis entro...

Scalar-field cosmologies with a generalized harmonic potential and matter with energy density $$\rho _m$$ ρ m , pressure $$p_m$$ p m , and barotropic equation of state (EoS) $$p_m=(\gamma -1)\rho _m, \; \gamma \in [0,2]$$ p m = ( γ - 1 ) ρ m , γ ∈ [ 0 , 2 ] in Kantowski–Sachs (KS) and closed Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are in...

We study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For...

For the fourth-order teleparallel \(f\left( T,B\right) \) theory of gravity, we investigate the cosmological evolution for the universe in the case of a spatially flat Friedmann–Lemaître–Robertson–Walker background space. We focus on the case for which \(f\left( T,B\right) \) is separable, that is, \(f\left( T,B\right) _{,TB}=0\) and \(f\left( T,B\...

We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to understand the evolution of solutions for various initial conditions as also to investigate the existence of a...

The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in $\mathbb{R}^4$. In this study, we investigate the behavior of trajectories in the presence of cosmological constant. It has been shown that the Szekeres system is a Hamiltonian dynamical system. It admits at least...

Study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For th...

In this work, we use an observational approach and dynamical system analysis to study the cosmological model recently proposed by Saridakis (2020), which is based on the modification of the entropy-area black hole relation proposed by Barrow (2020). The Friedmann equations governing the dynamics of the Universe under this entropy modification can b...

In this work we present for the first time the general solution of the temporal evolution equation arising from the matching of a conformally flat interior to the Vaidya solution. This problem was first articulated by Banerjee et al. (Phys Rev D 40:670, 1989) in which they provided a particular solution of the temporal equation. This simple exact s...

The derivation of conservation laws and invariant functions is an essential procedure for the investigation of nonlinear dynamical systems. In this study, we consider a two-field cosmological model with scalar fields defined in the Jordan frame. In particular, we consider a Brans-Dicke scalar field theory and for the second scalar field we consider...

We propose an Einstein-{\ae}ther scalar-tensor cosmological model. In particular in the scalar-tensor Action Integral we introduce the {\ae}ther field with {\ae}ther coefficients to be functions of the scalar field. This cosmological model extends previous studies on Lorentz-violating theories. For a spatially flat Friedmann--Lema\^{\i}tre--Roberts...

In this paper we study an axion model given by two canonical scalar fields $\phi_1,\,\phi_2$ coupled via a given potential $V(\phi_{1},\phi_{2})$. We introduce novel dynamical variables and dimensionless time variables, which have not been used in analyzing these cosmological dynamics where expansion normalized dynamical variables are usually adopt...

We consider a cosmological scenario endowed with an interaction between the universe’s dark components – dark matter and dark energy. Specifically, we assume the dark matter component to be a pressure-less fluid, while the dark energy component is a quintessence scalar field with Lagrangian function modified by the quadratic Generalized Uncertainty...

For the fourth-order teleparallel $f\left(T,B\right) $ theory of gravity, we investigate the cosmological evolution for the universe in the case of a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background space. We focus on the case for which $f\left(T,B\right) $ is separable, that is, $f\left(T,B\right) _{,TB}=0$ and $f\left(T,B\rig...

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic equation of state (EoS) with barotropic index $$\gamma $$ γ for the locally rotationally symmetric (LRS) Bianchi I and flat Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamic...

In this work we present for the first time the general solution of the temporal evolution equation arising from the matching of a conformally flat interior to the Vaidya solution. This problem was first articulated by Banerjee et al. (A. Banerjee, S. B. Dutta Choudhury, and Bidyut K. Bhui, Phys. Rev. D, 40 (670) 1989) in which they provided a parti...

We perform a detailed analysis on the asymptotic behavior of a multifield cosmological model with phantom terms. Specifically, we consider a Chiral-Phantom model consisting of two scalar fields with a mixed kinetic term, while one scalar field has a negative kinetic energy, that is, it has phantom properties. We show that the Hubble function can ch...

The derivation of conservation laws and invariant functions is an essential procedure for the investigation of nonlinear dynamical systems. In this study we consider a two-field cosmological model with scalar fields defined in the Jordan frame. In particular we consider a Brans-Dicke scalar field theory and for the second scalar field we consider a...

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $$\gamma $$ γ for locally rotationally symmetric (LRS) Bianchi III metric and open Friedmann–Lemaître–Robertson–Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dyn...

We consider a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background space with an ideal gas and a multifield Lagrangian consisting of two minimally coupled scalar fields which evolve in a field space of constant curvature. For this cosmological model we classify the potential function for the scalar fields such that variational poin...

We consider a cosmological scenario endowed with an interaction between the universe's dark components $-$ dark matter and dark energy. Specifically, we assume the dark matter component to be a pressureless fluid, while the dark energy component is a quintessence scalar field with Lagrangian function modified by the quadratic Generalized Uncertaint...

We perform a detailed analysis of the dynamics of a chiral-like cosmological model where the scalar fields can have negative kinetic terms. In particular, we study the asymptotic dynamics for the gravitational field equations for four different models in a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background space. When one of the s...

We apply the Painlev\'e Test for the Benney and the Benney-Gjevik equations which describe waves in falling liquids. We prove that these two nonlinear 1+1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-æther theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann–Lemaître–Robertson–Walker background space. We show that the theory admits cosmological solutions of...

Scalar field cosmologies with a generalized harmonic potential and a background matter given by a barotropic Equation of State (EoS) are investigated for Kantowski-Sachs metric and closed Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metrics. Using methods from the Theory of Averaging of Nonlinear Dynamical Systems and numerical simulations it is...

Scalar field cosmologies with a generalized harmonic potential and the background matter given by the barotropic Equation of State with barotropic index $\gamma$ are investigated for the Locally Rotationally Symmetric Bianchi III metric and for Open Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric. Using methods from the Theory of Averaging o...

Scalar field cosmologies with a generalized harmonic potential and a background matter with a barotropic Equation of State with barotropic index $\gamma$ are investigated for Locally Rotationally Symmetric Bianchi I and Flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metrics. Using methods from the Theory of Averaging of Nonlinear Dynamical Sy...

We present exact solutions in Einstein-aether theory in a static spherically symmetric background space with a spacelike aether field, as a difference with the usual selection of timelike aether field. We assume a coupling between the scalar field and the aether field introduced in the aether coefficients. The exact spacetimes describe hairy black...