arXiv subjects

J. Socorro

Publications and source records attributed to J. Socorro.

At least 19 recordsLinked to original sources

arXiv2026

Exact solutions using power law scalar potential in the Saez-Ballester-K-essence like theory

We investigate a K-essence like cosmological model whose scalar-field potential is constructed from a negative power-law S\'aez--Ballester potential. By means of a suitable field redefinition from $\phi$ to $\varphi$, we show that the resulting field equations acquire a mathematical structure analogous to that of a previously solved Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological model. This correspondence allows us to obtain exact classical solutions for both the scale factor and the scalar field within the Hamiltonian formalism. The resulting cosmological dynamics exhibits a late-time accelerated expansion, with the deceleration parameter approaching the asymptotic value $q\rightarrow -1$, characteristic of a de Sitter phase. At the quantum level, the corresponding Wheeler-DeWitt (WDW) equation is derived and exact quantum solutions are obtained. These results provide a consistent classical and quantum description of the cosmological evolution generated by this class of K-essence models. In this formalism, the scalar field remains as a cosmic background where the universe unfolds, which is glimpsed from the quantum solution perspective.

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arXiv2026

Power law scalar potential in the Saez-Ballester like theory: Exact solutions in the Bianchi type I case

We investigate exact anisotropic Bianchi type I cosmological solutions in a generalized S'aez--Ballester--K-essence-like theory containing two interacting scalar fields with quintessence, phantom, and mixed (quintom) kinetic sectors. The scalar-field self-interaction is described by inverse power-law potentials, which admit analytical solutions after an appropriate transformation of the field equations. The mixed kinetic interaction imposes nontrivial constraints on the model parameters, leading to six exact cosmological branches associated with the quintessence, phantom, and quintom scenarios. The exact solutions provide explicit expressions for the effective volume and scalar fields, allowing the reconstruction of the Hubble parameter, the deceleration parameter, and the effective equation-of-state parameter. Although the six branches exhibit distinct transient behaviors, all physically admissible solutions evolve toward the same asymptotic de Sitter attractor characterized by accelerated expansion. The analytical solutions reveal how the different kinetic sectors control the cosmological evolution while preserving a common late-time behavior. These results provide a unified analytical description of anisotropic cosmological dynamics in generalized scalar-field theories and may serve as a useful framework for investigating the role of interacting scalar fields in the early and late evolution of the Universe.

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arXiv2025

F(R,..) theories from the point of view of the Hamiltonian approach: non-vacuum Anisotropic Bianchi type I cosmological model

In this work, we will explore the effects of F(R) theories in the classical scheme using the anisotropic Bianchi Type I cosmological model with standard matter employing a barotropic fluid with equation of state $P=\gamma \rho$. In this work we present the classical solutions in two gauge, N=1 and $N=6ABCD=6\eta^3D$ obtaining some results that are usually used as ansatz to solve the Einstein field equation. For completeness, we present the solutions in vacuum as well.

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arXiv2024

Non commutative classical and Quantum fractionary Cosmology: Anisotropic Bianchi Type I case

In this work, we will explore the effects of non-commutativity in fractional classical and quantum schemes using the anisotropicc Bianchi Type I cosmological model coupled to a scalar field in the K-essence formalism. We introduce non-commutative variables considering that all minisuperspace variables $q^i_{nc}$ do not commute, so the symplectic structure was modified, resulting in some changes with respect to the traditional formalism. In the quantum regime, the probability density presents a new structure in the scalar field corresponding to the value of the non-commutative parameter.

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arXiv2024

Non commutative classical and Quantum fractionary Cosmology: FRW case

In this work we shall explore the effects of non commutativity in fractional classical and quantum schemes using the flat Friedmmann-Robertson-Walker (FRW) cosmological model coupled to a scalar field in the K-essence formalism. In previous work we have obtained the commutative solutions in both regimes into the fractional framework. Here we introduce noncommutative variables, considering that all minisuperspace variables $\rm q^i_{nc}$ do not commute, so the symplectic structure was modified. In the quantum regime, the probability density presents new structure in the scalar field corresponding to the value of the non-commutative parameter, in the sense that this probability density undergoes a shift back to the direction of the scale factor, causing classical evolution to arise earlier than in the commutative world.

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arXiv2023

Anisotropic fractional cosmology: K-essence theory

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $β=\frac{2α}{2α- 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $ω_{X} \in [0,1]$, the order belongs to the interval $1\leq β\leq 2$, and when $ω_{X}\in[-1,0)$, the order belongs to the interval $0< β\leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(Ω,ϕ)$ and its corresponding momenta $(Π_Ω, Π_ϕ)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(τ)$, however in the dust era we found a closed solution in the gauge time $τ$. Keywords: Fractional derivative, Fractional Quantum Cosmology; K-essence formalism; Classical and Quantum exact solutions.

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arXiv2023

Noncommutative effective LQC: A (pre-)inflationary dynamics investigation

We conduct a (pre-)inflationary dynamics study within the framework of a simple noncommutative extension of effective loop quantum cosmology -- put forward recently by the authors -- which preserves its key features (in particular, the quantum bounce is maintained). A thorough investigation shows that the (pre-)inflationary scenario associated to the chaotic quadratic potential is in the overall the same as the one featured in standard loop quantum cosmology (which reinforces the conclusion reached by the authors in a preliminary analysis). Hence, this (pre-)inflationary scenario does not easily distinguish between standard loop quantum cosmology and the aforementioned noncommutative scheme. It is argued that a particular tuning of the noncommutativity parameter could accommodate for subtle effects at the level of primordial perturbations (the hybrid quantization framework being a tentative route of analysis).

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arXiv2023

Quintom fields from chiral anisotropic cosmology

In this paper we present an analysis of a chiral anisotropic cosmological scenario from the perspective of quintom fields. In this setup quintessence and phantom fields interact in a non-standard (chiral) way within an anisotropic Bianchi type I background. We present our examination from two fronts: classical and quantum approaches. In the classical program we find analytical solutions given by a particular choice of the emerged relevant parameters. Remarkably, we present an explanation of the ''big-bang'' singularity by means of a ''big-bounce''. Moreover, isotropization is in fact reached as the time evolves. On the quantum counterpart the Wheeler-DeWitt equation is analytically solved for various instances given by the same parameter space from the classical study, and we also include the factor ordering $\rm Q$. Having solutions in this scheme we compute the probability density, which is in effect damped as the volume function and the scalar fields evolve; and it also tends towards a flat FLRW framework when the factor ordering constant $\rm Q \ll 0$. This result might indicate that for a fixed set of parameters, the anisotropies quantum-mechanically vanish for very small values of the parameter $\rm Q$. Finally, classical and quantum solutions reduce to their flat FLRW counterparts when the anisotropies vanish.

gr-qc↗

arXiv2023

Quantum fractionary cosmology: K-essence theory

Using a particular form of the quantum K-essence scalar field, we show that in the quantum formalism, a fractional differential equation in the scalar field variable, for some epochs in the Friedmann-Lemaître-Robertson-Walker (FLRW) model (radiation and inflation-like epochs, for example), appears naturally. In the classical analysis, the kinetic energy of scalar fields can falsify the standard matter in the sense that we obtain the time behavior for the scale factor in all scenarios of our Universe by using the Hamiltonian formalism, where the results are analogous to those obtained by an algebraic procedure in the Einstein field equations with standard matter. In the case of the quantum Wheeler-DeWitt (WDW) equation for the scalar field $ϕ$, a fractional differential equation of order $β=\frac{2α}{2α-1}$ is obtained. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; that is to say, when $ ω_X \in [0,1]$, the order belongs to the interval $1\leq β\leq 2$, and when $ ω_X \in [-1,0)$, the order belongs to the interval $0< β\leq 1$. The corresponding quantum solutions are also given.

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arXiv2022

Quintom fields from chiral K-essence cosmology

In this paper, we present an analysis of a chiral cosmological scenario from the perspective of K-essence formalism. In this setup, several scalar fields interact within the kinetic and potential sectors. However, we only consider a flat Friedmann--Robertson--Lama\^ıtre--Walker universe coupled minimally to two quintom fields: one quintessence and one phantom. We examine a classical cosmological framework, where analytical solutions are obtained. Indeed, we present an explanation of the ``big-bang'' singularity by means of a ``big-bounce''. Moreover, having a barotropic fluid description and for a particular set of parameters, the phantom line is in fact crossed. Additionally, for the quantum counterpart, the Wheeler--DeWitt equation is analytically solved for various instances, where the factor-ordering problem has been taken into account (measured by the factor Q). Hence, this approach allows us to compute the probability density of the previous two classical subcases. It turns out that its behavior is in effect damped as the scale factor and the scalar fields evolve. It also tends towards the phantom sector when the factor ordering constant $\rm Q\ll 0$.

gr-qc↗

arXiv2021

Anisotropic chiral cosmology: exact solutions

In this work, we investigate the anisotropic Bianchi type I cosmological model in the chiral setup, in a twofold manner. Firstly, we consider a quintessence plus a k-essence like model, where two scalar fields but only one potential term is considered. Secondly, we look at a model where in addition to the two scalar fields the two potential terms are taken into account as well as the standard kinetic energy and the mixed term. Regarding this second model, it is shown that two possible cases can be studied: a quintom like case and a quintessence like case. In each of the models, we were able to find both classical and quantum analytical solutions.

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arXiv2021

Classical and quantum exact solutions for a FRW in chiral like cosmology

In this work, first, we study a flat Friedmann-Robertson-Walker Universe with two scalar fields but only one potential term, which can be thought as a simple quintessence plus a K-essence model. Employing the Hamiltonian formalism we are able to obtain the classical and quantum solutions. The second model studied, is also a flat Friedmann-Robertson-Walker Universe with two scalar fields, with the difference that the two potentials are considered as well as the standard kinetic energy and the mixed term (chiral field approach). Regarding this second model, it is shown that setting to zero the coefficient accompanying the mixed momenta term, two possible cases can be studied: a quintom like case ($m^{12}_{+}$) and a quintessence like case ($m^{12}_{-}$). For both scenarios classical and quantum solutions are presented.

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arXiv2021

Noncommutative Effective LQC: inclusion of potential term

We construct and study a simple noncommutative scheme (theta-deformation) for the effective Loop Quantum Cosmology of the flat Friedmann-Lemaître-Robertson-Walker model in the presence of a homogeneous scalar field $ϕ$ with a potential $\mathcal{V}(ϕ)=\frac{1}{2}m^2ϕ^2$. We first conduct a simple analysis from the corresponding Hamilton equations of motion considering a generic term $\mathcal V(ϕ)$. It is observed that the characteristic Big Bounce of Loop Quantum Cosmology is preserved under such noncommutative extension. When specializing to the quadratic case, numerical solutions to the corresponding Hamilton equations exhibiting an early inflationary epoch with a sufficiently large number of e-foldings are found. It is concluded that, in this noncommutative setup, solutions exist which are in the overall compatible with the early universe predicted by standard (effective) Loop Quantum Cosmology (i.e. a bouncing and inflationary early universe). The issue of the genericness of a sufficiently long inflationary period on the space of solutions in this noncommutative construct remains to be addressed.

gr-qc↗

arXiv2020

Cosmological volume acceleration in dust epoch: using scaling solutions and variable cosmological term $Λ(t)$ within an anisotropic cosmological model

Under the premise that the current observations of the cosmic microwave background radiation set a very stringent limit to the anisotropy of the universe, we consider an anistropic model in the presence of a barotropic perfect fluid and a homogeneous scalar field, which transits to a flat FRW cosmology for late times in a dust epoch, presenting an accelerated volume expansion. Furtheremore, the scalar field is identified with a varying cosmological term via $V(ϕ(t))=2Λ(t)$. Exact solutions to the EKG system are obtained by proposing an anisotropic extension of the scaling solutions scenario: $\rmρ\sim η^{-n},\ ρ_ϕ\sim η^{-m}$, with $\rmη^3=a_1a_2a_3$ the volume function of the anistropic model ($\rm a_1,\, a_2,\, a_3$ being the scale factors).

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arXiv2019

Noncommutative Friedmann Equations in Effective LQC

In this work we construct a noncommutative version of the Friedmann equations in the framework of effective loop quantum cosmology, extending and applying the ideas presented in a previous proposal by some of the authors. The model under consideration is a flat FRW spacetime with a free scalar field. First, noncommutativity in the momentum sector is introduced. We establish the noncommutative equations of motion and obtain the corresponding exact solutions. Such solutions indicate that the bounce is preserved, in particular, the energy density is the same as in standard LQC. We also construct a noncommutative version of the modified Friedmann equations and argue that, as a consequence of noncommutativity, an effective potential arises. This, in turn, leads us to investigate the possibility of an inflationary era. Finally, we obtain the Friedmann and the Raychaudhuri equations when implementing noncommutativity in the configuration sector. In this case, no effective potential is induced.

gr-qc↗

arXiv2019

Supersymmetric Quantum Mechanics: two factorization schemes, and quasi-exactly solvable potentials

We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its supercharges, which are defined as matrix or differential operators. We show that, although most of the SUSY partners of one-dimensional Schrödinger problems have already been found,there are still some unveiled aspects of the factorization procedure which may lead to richer insights of the problem involved.

quant-ph↗

arXiv2018

Classical and quantum exact solutions for a FRW multi-scalar field cosmology with an exponential potential driven inflation

A flat Fiedmann-Robertson-Walker (FRW) multi-scalar field cosmology is studied with a particular potential of the form $ \rm V(ϕ,σ)=V_0 e^{-λ_1 ϕ-λ_2 σ}$, which emerges as a relation between the time derivatives of the scalars field momenta. Classically, by employing the Hamiltonian formalism of two scalar fields $\rm(ϕ,σ)$ with standard kinetic energy, exact solutions are found for the Einstein-Klein-Gordon (EKG) system for different scenarios specified by the parameter $\rmλ^2=λ_1^2+λ_2^2$, as well as the e-folding function $\rm N_{e}$ which is also computed. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables.

gr-qc↗

arXiv2018

Hamilton's approach in cosmological inflation with an exponential potential and its observational constraints

The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general potential $\rm V(ϕ)$ in the scalar field inflation scenario. The Bohmian approach (a WKB-like formalism) was employed in order to constraint a generic form of potential to the most suited to drive inflation, from here a family of potentials emerges; in particular we select an exponential potential as the first non trivial case and remains the object of interest of this work. The solution to the Wheeler-DeWitt (WDW) equation is also obtained for the selected potential in this scheme. Using Hamilton's approach and equations of motion for a scalar field $\rm ϕ$ with standard kinetic energy, we find the exact solutions to the complete set of Einstein-Klein-Gordon (EKG) equations without the need of the slow-roll approximation (SR). In order to contrast this model with observational data (Planck 2018 results), the inflationary observables: the tensor-to-scalar ratio and the scalar spectral index are derived in our proper time, and then evaluated under the proper condition such as the number of e-folding corresponds exactly at 50-60 before inflation ends. The employed method exhibits a remarkable simplicity with rather interesting applications in the near future.

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