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J. Socorro

Publications and source records attributed to J. Socorro.

At least 37 records · Page 2Linked to original sources
arXiv2018

Cosmologies with scalar fields from higher dimensions applied to Bianchi type $\rm VI_{h=-1}$ model: classical and quantum solutions

In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. The corresponding action in four dimensions is similar to the action of K-essence theories. This approach is applied to anisotropic cosmological Bianchi type $VI_{(h=-1)}$ model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. The classical Einstein field equations give us a hidden symmetry, corresponding to equal radii B=C, which permits us to solve exactly the equations of motion. With this hidden symmetry, then we solve the FRW, finding that the scale factor goes to B radii. Also the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology is solved. Bohm's formalism for this cosmological model is revisited too.

gr-qc↗
arXiv2017

Cosmological super inflation using Hamilton's approach

The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a particular potential $\rm V(ϕ)=V_0 e^{-\sqrt{3} ϕ}$ in the quintessence field scenario, which emerges in the supersymmetric quantum mechanics (SUSY) formalism. Using Hamilton's approach for a scalar field $ϕ$ with standard kinetic energy, and the Hamilton equations, we find exact solutions to the complete set of the Einstein-Klein-Gordon equations without the need of the slow-roll conditions in order to model the inflation phenomenon. We find that the solutions are in good agreement with the inflationary conditions such as the e-folding function ${\cal N}$ which corresponds to the $Ω$ function in the Misner parametrization for the scale factor $\rm A(t)=e^{Ω(t)}$ when evaluated in $\rm Δt$, which is the time interval for the inflation period. The acceleration of the scale factor was computed and it was found to be positive for the inflation period with a range of values for the parameters of the model. Quantum solution from the Wheeler-DeWitt equation is presented, where the wave function in relation to the evolution of the scale factor, shows that for this period of time at larger values of $\rm A$ and for any value of scalar-field $\rm φ$, the wave function is peaked.

gr-qc↗
arXiv2017

Scalar potentials with Multi-scalar fields from quantum cosmology and supersymmetric quantum mechanics

The Multi-scalar field cosmology of the anisotropic Bianchi type I model is used in order to construct a family of potentials that are the best suited to model the inflation phenomenon. We employ the quantum potential approach to quantum mechanics due to Bohm in order to solve the corresponding Wheeler-DeWitt equation; which in turn enables us to restrict sensibly the aforementioned family of potentials. Supersymmetric Quantum Mechanics (SUSYQM) is also employed in order to constrain the superpotential function, at the same time the tools from SUSY Quantum Mechanics are used to test the family of potentials in order to infer which is the most convenient for the inflation epoch. For completeness solutions to the wave function of the universe are also presented.

gr-qc↗
arXiv2016

Time-dependent toroidal compactification proposals and the Bianchi type I model: classical and quantum solutions

In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. This approach is applied to anisotropic cosmological Bianchi type I model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Under this approach, we present an isotropization mechanism for the Bianchi I cosmological model through the analysis of the ratio between the anisotropic parameters and the volume of the Universe which in general keeps constant or runs into zero for late times. We also find that the presence of extra dimensions in this model can accelerate the isotropization process depending on the momenta moduli values. Finally, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology.

gr-qc↗
arXiv2015

Variable cosmological term $Λ(t)$

We present the case of time-varying cosmological term $Λ(t)$. The main idea arises by proposing that as in the cosmological constant case, the scalar potential is identified as $ V(ϕ)=2Λ$, with $Λ$ a constant, this identification should be kept even when the cosmological term has a temporal dependence, i.e., $ V(ϕ(t))=2Λ(t)$. We Use the Lagrangian formalism for a scalar field $ϕ$ with standard kinetic energy and arbitrary potential $V(ϕ)$ and apply this model to the Friedmann-Robertson-Walker (FRW)cosmology. Exact solutions of the field equations are obtained by a special ansatz to solve the Einstein-Klein-Gordon equation and a particular potential for the scalar field and barotropic perfect fluid. We present the evolution on this cosmological term with different scenarios.

physics.gen-ph↗
arXiv2015

Time-dependent toroidal compactification proposals and the Bianchi type II model: classical and quantum solutions

In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus without the contributions of fluxes as first approximation. This approach is applied to anisotropic cosmological Bianchi type II model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Also, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology and we claim that these quantum solution are generic in the moduli scalar field for all Bianchi Class A models. Also we gives the relation to these solutions for asymptotic behavior to large argument in the corresponding quantum solution in the gravitational variables and is compared with the Bohm's solutions, finding that this corresponds to lowest-order WKB approximation.

gr-qc↗
arXiv2014

Classical Bianchi type I cosmology in K-essence theory

We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid modeling the usual matter content and with cosmological constant. The classical solutions for any but the stiff fluid and without cosmological constant are found in closed form, using a time transformation. We also present the solution whith cosmological constant and some particular values of the barotropic parameter. We present the possible isotropization of the cosmological model, using the ratio between the anisotropic parameters and the volume of the universe and show that this tend to a constant or to zero for different cases. We include also a qualitative analysis of the analog of the Friedmann equation.

gr-qc↗
arXiv2013

Quintom potentials from quantum cosmology using the FRW cosmological model

We construct the quintom potential of dark energy models in the framework of spatially flat Friedmann-Robertson Walker universe in the inflationary epoch, using the Bohm like approach, known as amplitude-real-phase. We find some potentials for which the wave function of the universe is found analytically and we have obtained the classical trajectories in the inflation era.

gr-qc↗
arXiv2013

FRW in cosmological self-creation theory

We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $\rm <[\{1}ϕT^{μνM}+T^{μν}(ϕ)>]_{;ν}=0$. We take as a first model the flat FRW metric and with the law of variation for Hubble's parameter proposal by Berman \cite{Berman}, we find solutions to the Einstein field equations by the cases: inflation ($γ=-1$), radiation ($γ=\{1}{3}$), stiff matter ($γ=1$). For the Inflation case the scalar field grows fast and depends strongly of the constant $\rm M_{γ=-1}$ that appears in the solution, for the Radiation case, the scalar stop its expansion and then decrease perhaps due to the presence of the first particles. In the Stiff Matter case, the scalar field is decreasing so for a large time, $ϕ\rightarrow0$. In the same line of classical solutions, we find an exact solution to the Einstein field equations for the stiff matter $(γ=1)$ and flat universe, using the Hamilton-Jacobi scheme.

gr-qc↗
arXiv2013

Quintom phase-space: beyond the exponential potential

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.

gr-qc↗
arXiv2013

FRW in cosmological self-creation theory: Hamiltonian approach

We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $\rm[\frac{1}ϕ(8πT^{μν(M)}+T^{μν(ϕ)})]_{;ν}=0$. We take as a first model the flat FRW metric in the Hamilton-Jacobi scheme and we present the Lagrange-Charpit approach in order to find classical solutions. In the quantum scheme, once we determine the characteristic surfaces, the quantum solution is obtained. These two classes of solutions are found for all values of the barotropic parameter $γ$.

gr-qc↗
arXiv2011

Cosmological Bianchi Class A models in Sáez-Ballester theory

We use the Sáez-Ballester (SB) theory on anisotropic Bianchi Class A cosmological model, with barotropic fluid and cosmological constant, using the Hamilton or Hamilton-Jacobi approach. Contrary to claims in the specialized literature, it is shown that the Sáez-Ballester theory cannot provide a realistic solution to the dark matter problem of Cosmology for the dust epoch, without a fine tunning because the contribution of the scalar field in this theory is equivalent to a stiff fluid (as can be seen from the energy--momentum tensor for the scalar field), that evolves in a different way as the dust component. To have similar contributions of the scalar component and the dust component implies that their past values were fine tunned. So, we reinterpreting this null result as an indication that dark matter plays a central role in the formation of structures and galaxy evolution, having measureable effects in the cosmic microwave bound radiation, and than this formalism yield to this epoch as primigenius results. We do the mention that this formalism was used recently in the so called K-essence theory applied to dark energy problem, in place to the dark matter problem. Also, we include a quantization procedure of the theory which can be simplified by reinterpreting the theory in the Einstein frame, where the scalar field can be interpreted as part of the matter content of the theory, and exact solutions to the Wheeler-DeWitt equation are found, employing the Bianchi Class A cosmological models.

gr-qc↗
arXiv2010

Inflation from Supersymmetric Quantum Cosmology

We derive a special scalar field potential using the anisotropic Bianchi type I cosmological model from canonical quantum cosmology under determined conditions in the evolution to anisotropic variables $β_\pm$. In the process, we obtain a family of potentials that has been introduced by hand in the literature to explain cosmological data. Considering supersymmetric quantum cosmology, this family is scanned, fixing the exponential potential as more viable in the inflation scenario $\rm V (ϕ) = V_0 \,e^{-\sqrt{3}ϕ}$.

gr-qc↗
arXiv2009

Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology

Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type I cosmological model, coupled to a scalar field, cosmological term and barotropic perfect fluid. We introduce noncommutative scale factors, considering that all minisuperspace variables $\rm q^i$ do not commute, so the symplectic structure was modified. In the classical regime, it is shown that the anisotropic parameter $\rm β_{\pm nc}$ and the field $ϕ$, for some value in the $λ_{eff}$ cosmological term and noncommutative $θ$ parameter, present a dynamical isotropization up to a critical cosmic time $t_{c}$; after this time, the effects of isotropization in the noncommutative minisuperspace seems to disappear. In the quantum regimen, the probability density presents a new structure that corresponds to the value of the noncommutativity parameter.

gr-qc↗
arXiv2009

Classical and quantum Cosmology of the Sáez-Ballester theory

We study the generalization of the Sáez-Ballester theory applied to a flat FRW cosmological model. Classical exact solutions up to quadratures are easily obtained using the Hamilton-Jacobi approach. Contrary to claims in the specialized literature, it is shown that the Sáez-Ballester theory cannot provide a realistic solution to the dark matter problem of Cosmology. Furthermore the quantization procedure of the theory can be simplified by reinterpreting the theory in the Einstein frame, where the scalar field can be interpreted as part of the matter content of the theory, in this approach, exact solutions are also found for the Wheeler-DeWitt equation in the quantum regime.

gr-qc↗
arXiv2008

Towards noncommutative supersymmetric quantum cosmology

Using the factorization approach of quantum mechanics, we obtain a family of iso-spectral scalar potentials for noncommutative quantum cosmology. The family we build is based on a scattering Wheeler-DeWitt solution for the potential $V(ϕ)=V_0e^{-λϕ}$. We analyze the effects of noncommutativity on the iso-potentials and the possible relationship between noncommutativity and dark energy.

hep-th↗
arXiv2008

On Noncommutative Minisuperspace and the Friedmann equations

In this paper we present noncommutative version of scalar field cosmology. We find the noncommutative Friedmann equations as well as the noncommutative Klein-Gordon equation. Interestingly the noncommutative contributions are only present up to second order in the noncommutitive parameter. Finally we conclude that if we want a noncommutative minisuperspace with a constant noncommutative parameter as viable phenomenological model, the noncommuative parameter is very small.

gr-qc↗