Deformed phase space in a two-dimensional minisuperspace model

Sepangi, H. R.; Shakerin, Bahram; Vakili, Babak

doi:10.1088/0264-9381/26/6/065003

Cited by 12 publications

(13 citation statements)

References 68 publications

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“…In more than one dimension, it can be shown that the generalized Heisenberg algebra corresponding to GUP is defined by the following commutation relations [7,8] […”

Section: Gup Casementioning

confidence: 99%

Multi-dimensional cosmology and GUP

Zeynali

Darabi

Motavalli

2012

J. Cosmol. Astropart. Phys.

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We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and d-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology in commutative and GUP cases and obtain the corresponding exact solutions for negative and positive cosmological constants. It is shown that for negative cosmological constant, the commutative and GUP cases result in finite size universes with smaller size and longer ages, and larger size and shorter age, respectively. For positive cosmological constant, the commutative and GUP cases result in infinite size universes having late time accelerating behavior in good agreement with current observations. The accelerating phase starts in the GUP case sooner than the commutative case. In both commutative and GUP cases, and for both negative and positive cosmological constants, the internal space is stabilized to the sub-Planck size, at least within the present age of the universe. Then, we study the quantum cosmology by deriving the Wheeler-DeWitt equation, and obtain the exact solutions in the commutative case and the perturbative solutions in GUP case, to first order in the GUP small parameter, for both negative and positive cosmological constants. It is shown that good correspondence exists between the classical and quantum solutions.

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“…In more than one dimension, it can be shown that the generalized Heisenberg algebra corresponding to GUP is defined by the following commutation relations [7,8] […”

Section: Gup Casementioning

confidence: 99%

Multi-dimensional cosmology and GUP

Zeynali

Darabi

Motavalli

2012

J. Cosmol. Astropart. Phys.

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“…where A 1 , A 2 , B 1 , B 2 are constants of integration. By substituting (19) into Hamiltonian constraint (15), it is obtained that…”

Section: The Classical Modelmentioning

confidence: 99%

“…where E pl = hc 5 G ≈ 1.22 × 10 19 GeV is the (unreduced) Planck energy. The classical partition function for the linear harmonic oscillator (LHO) of mass m and frequency ω is:…”

Section: Thermodynamics Of the Modelmentioning

confidence: 99%

Two-oscillator Kantowski–Sachs model of the Schwarzschild black hole interior

2016

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In this paper the interior of the Schwarzschild black hole, which is presented as a vacuum homogeneous and anisotropic Kantowski-Sachs minisuperspace cosmological model, is considered. Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model will be presented in a classical, a p-adic and a noncommutative case. Then, within the standard quantum approach Wheeler-DeWitt equation and its general solutions, i.e. a wave function of the model, will be written, and then an adelic wave function will be constructed. Finally, thermodynamics of the model will be studied by using the Feynman-Hibbs procedure.

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“…For example, if in a model field theory the fields are taken as noncommutative, as has been done in [35,36], the resulting effective theory predicts the same Lorentz violation as a field theory in which the coordinates are considered as noncommutative [37][38][39]. As a further example, it is well known that string theory can be used to suggest a modification to the bracket structure of coordinates, also known as GUP [34] which is used to modify the phase-space structure [40][41][42][43][44][45]. Over the years, a large number of works on noncommutative fields [25][26][27][28][29] have been inspired by noncommutative geometry model theories [31][32][33].…”

Section: Phase-space Deformation: a Procedures For Quantizationmentioning

confidence: 99%

“…(1). Here we will examine a new kind of modification in the phase-space structure inspired by relation (1), much the same as has been done in [25][26][27][28][29][40][41][42][43][44][45]59]. In what follows we introduce noncommutativity based on κ-Minkowskian space and study its consequences on the de Sitter and dusty FRW cosmologies.…”

Section: Phase-space Deformation: a Procedures For Quantizationmentioning

confidence: 99%

A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization

2009

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We employ the familiar canonical quantization procedure in a given cosmological setting to argue that it is equivalent to and results in the same physical picture if one considers the deformation of the phase-space instead. To show this we use a probabilistic evolutionary process to make the solutions of these different approaches comparable. Specific model theories are used to show that the independent solutions of the resulting Wheeler-DeWitt equation are equivalent to solutions of the deformation method with different signs for the deformation parameter. We also argued that since the Wheeler-DeWitt equation is a direct consequence of diffeomorphism invariance, this equivalence is only true provided that the deformation of phase-space does not break such an invariance.

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Deformed phase space in a two-dimensional minisuperspace model

Cited by 12 publications

References 68 publications

Multi-dimensional cosmology and GUP

Multi-dimensional cosmology and GUP

Two-oscillator Kantowski–Sachs model of the Schwarzschild black hole interior

A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization

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