Topics in Supersymmetric and Noncommutative Quantum Cosmology

García‐Compeán, Hugo; Obregón, O.; Ramı́rez, C.

doi:10.3390/universe7110434

Cited by 10 publications

(9 citation statements)

References 69 publications

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“…In what concerns SUSY quantum cosmology, there have been a few books in the past 30 years or so [73,18,19] plus selected reviews on the different procedures that were constructed and subsequently promoted [74,75,76,77,78,79,80,81,82,83,84]. Likewise chapters (and sections) about SUSY quantum cosmology in well known textbooks concerning quantum gravity [85,86,87,88].…”

Section: Discussionmentioning

confidence: 99%

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

Jalalzadeh,

Rasouli,

Moniz

2022

Preprint

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In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of N = 2 supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate the value of this promising tool. Concretely, we take a spatially flat FRW model in the presence of a single scalar field, minimally coupled to gravity. Then, we extract the associated Schrödinger-Wheeler-DeWitt equation, allowing for a particular scope of factor ordering. Subsequently, we compute the corresponding supersymmetric partner Hamiltonians, H1 and H2. Moreover, we point out how the shape invariance property can be employed to bring a relation among several factor orderings choices for our Schrödinger-Wheeler-DeWitt equation. The ground state is retrieved, and the excited states easily written. Finally, the Hamiltonians, H1 and H2 are explicitly presented within a N = 2 supersymmetric quantum mechanics framework.

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Section: Discussionmentioning

confidence: 99%

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

Jalalzadeh,

Rasouli,

Moniz

2022

Preprint

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“…In the rest of this section, we will note the formulation of noncommutative system using undeformed canonical variables. A similar formulation is already known in quantum cosmology, the technique required to find the WDW equation [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][31][32][33].…”

Section: Classical Noncommutative Bicosmologymentioning

confidence: 99%

Classical and quantum bicosmology with noncommutativity

Kan¹,

Aoyama²,

Shiraishi³

2022

Class. Quantum Grav.

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Recently, Falomir, Gamboa, Mendez, Gondolo and Maldonado proposed a bicosmology scenario [1-4] for solving some cosmological problems related to inflation, dark matter, and thermal history of the universe. Their plan is to introduce noncommutativity into the momentum space of the two scale factors. In the present paper, we revisit their model and first consider exact classical solutions in the model with constant noncommutativity between dynamical variables and between canonical momenta. We also hypothesize that the noncommutativity appears when the scale factors are small, and show the behavior of the classical solution in that case with momentum-space noncommutativity. Finally, we write down the Wheeler-DeWitt equation in that case and examine the behavior of the solution.

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“…The classical Hamiltonian constraint is canonically quantized and results in the so called Wheeler-DeWitt (WDW) equation [9,10]. The solutions of this equation are wave functionals defined in superspace called wave functions of the Universe in quantum cosmology (for some reviews, see [11][12][13][14]). Although the interpretation of these solutions is still an ongoing debate (see for example [15] for a recent discussion) the ratio of two solutions can be interpreted as a probability to obtain a transition between both configurations.…”

Section: Introductionmentioning

confidence: 99%

Lorentzian vacuum transitions with a generalized uncertainty principle

García‐Compeán¹,

Mata-Pacheco²

2022

Class. Quantum Grav.

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The vacuum transition probabilities between to minima of a scalar field potential in the presence of gravity are studied using the Wentzel-Kramers-Brillouin approximation. First we propose a method to compute these transition probabilities by solving the Wheeler-DeWitt equation in a semi-classical approach for any model of superspace that contains terms of squared as well as linear momenta in the Hamiltonian constraint generalizing in this way previous results. Then we apply this method to compute the transition probabilities for a Friedmann-Lemaitre-Robertson-Walker metric with positive and null curvature and for the Bianchi III metric when the coordinates of minisuperspace obey a Standard Uncertainty Principle and when a Generalized Uncertainty Principle is taken into account. In all cases we compare the results and found that the effect of considering a Generalized Uncertainty Principle is that the probability is enhanced at first but it decays faster so when the corresponding scale factor is big enough the probability is reduced. We also consider the effect of anisotropy and compare the result of the Bianchi III metric with the flat FLRW metric which corresponds to its isotropy limit and comment the differences with previous works.

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Topics in Supersymmetric and Noncommutative Quantum Cosmology

Cited by 10 publications

References 69 publications

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

Classical and quantum bicosmology with noncommutativity

Lorentzian vacuum transitions with a generalized uncertainty principle

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