Quintom Potential from Quantum Anisotropic Cosmological Models

Socorro, J.; Rodríguez, Paulo A.; Núñez-Soltero, O.; Hernández, Rafael; Espinoza-García, Abraham

doi:10.5772/52054

Cited by 5 publications

(7 citation statements)

References 33 publications

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“…We claim that this solutions is the same for all Bianchi Class A cosmological models, because the Hamiltonian operator in (29) can be written in separated way aŝ …”

Section: Quantum Wheeler-dewitt (Wdw) Formalismmentioning

confidence: 99%

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

Socorro

Sesma

2016

Eur. Phys. J. Plus

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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.

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“…We claim that this solutions is the same for all Bianchi Class A cosmological models, because the Hamiltonian operator in (29) can be written in separated way aŝ …”

Section: Quantum Wheeler-dewitt (Wdw) Formalismmentioning

confidence: 99%

“…We present the main ideas of this formalism to solve the WDW equation, you can see [29]. Also we use the hidden symmetry in the potential U for this model [30,31], which seems to be a general property of the Bianchi models.…”

Section: Quantum Wheeler-dewitt (Wdw) Formalismmentioning

confidence: 99%

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

Socorro

Sesma

2016

Eur. Phys. J. Plus

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“…Moreover, the best candidates for quantum solutions are those that have a damping behavior with respect to the scale factor, since only such wave functions allow for good solutions when using a Wentzel-Kramers-Brillouin (WKB) approximation for any scenario in the evolution of our Universe [73,74]. Furthermore, in the context of a single scalar field a family of scalar potentials is obtained in the Bohmian formalism [53,75], or supersymmetric quantum cosmology [76][77][78], where among others a general potential of the form V(φ) = V 0 e −λφ is examined. This work is arranged as follows.…”

Section: Introductionmentioning

confidence: 99%

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

Socorro,

Pérez-Payán,

Hernández

et al. 2020

Preprint

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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 two possible cases can be studied: a quintom like case and a quintessence like case. For both scenarios classical and quantum solutions are presented.

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“…where W ( µ ) is an amplitude which varies slowly and S( µ ) is the phase whose variation is faster that the amplitude, this allows us to obtain eikonal -like equations. The term µ is the dynamical variables of the minisuperspace which are µ = a, c. This formalism is known as the Bohm's formalism too [12,[16][17][18]. So, the equation (41a) is transformed under the expression (48) into…”

Section: Quantum Schemementioning

confidence: 99%

“…The term ℓ is the dynamical variables of the minisuperspace which are ℓ = , . This formalism is known as Bohm's formalism too [27,[32][33][34]. So, (49a) is transformed under expression (59) into…”

Section: Bohm's Formalismmentioning

confidence: 99%

Cosmologies with Scalar Fields from Higher Dimensions Applied to Bianchi Type VIh=-1 Model: Classical and Quantum Solutions

Socorro

Sesma

Pimentel

2018

Advances in High Energy Physics

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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 (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 the equality between two radii B=C, which permits us to solve exactly the equations of motion. One relation between the scale factors (A,C) via the solutions is found. With this hidden symmetry, then we solve the FRW model, 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, building a wavepacket when the scalar fields have a hyperbolic behavior, obtaining some qualitative results when we analyze the projection plane to the wall formed by the probability density. Bohm's formalism for this cosmological model is revisited too.

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Quintom Potential from Quantum Anisotropic Cosmological Models

Cited by 5 publications

References 33 publications

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

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

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

Cosmologies with Scalar Fields from Higher Dimensions Applied to Bianchi Type VIh=-1 Model: Classical and Quantum Solutions

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