Quantum Cosmological Perfect Fluid Models

Alvarenga, F. G.; Fabris, J. C.; Lemos̀, Nivaldo A.; Monerat, G. A.

doi:10.1023/a:1015986011295

Cited by 176 publications

(219 citation statements)

References 18 publications

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“…Another way by which one may compute the wave-function of the Universe is by directly solving the Wheeler-DeWitt equation [1]. The wave-function of the Universe for some important models have been computed using this approach [5][6][7][8][9][10].Several important theoretical results and predictions in quantum cosmology have been obtained with a negative cosmological constant [11], [12] and [3]. Besides that, we think it is important to understand more about such models which represent bound Universes (analogous to uni-dimensional atoms, in the present situation).…”

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confidence: 99%

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“…where p a and p T are the momenta canonically conjugated to a and T the latter being the canonical variable associated to the fluid [10].…”

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Notes on the quantization of FRW model in the presence of a cosmological constant and radiation

Monerat¹,

Silva²,

Oliveira‐Neto³

et al. 2005

Braz. J. Phys.

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In the present work, we use the formalism of quantum general relativity in order to quantize a FriedmannRobertson-Walker model in the presence of a negative cosmological constant and radiation. The model has spatial sections with positive constant curvature. The wave-function of the model satisfies a Wheeler-DeWitt equation, for the scale factor, which has the form of the Schrödinger's equation for the quartic anharmonic oscillator. We find the eigenvalues and eigenfunctions by using a method first developed by Chhajlany and Malnev. After that, we use the eigenfunctions in order to construct wave-packets for evaluating the time-dependent, expected value of the scale factor. We find that, the expected value of the scale factor oscillates between maximum and minimum values. Since the scale factor never vanishes, we conclude that the model does not have a singularity.One of the motivations for the quantization of cosmological models was that of avoiding the initial Big Bang singularity. Since the pioneering work in quantum cosmology due to DeWitt [1], workers in this field have been attempting to prove that quantum cosmological models entail only regular space-times. An important contribution to this issue was given by Hartle and Hawking [2], who proposed the no-boundary boundary condition, which selects only regular space-times to contribute to the wave-function of the Universe, derived in the path integral formalism. Therefore, by construction, the no-boundary wave-functions are everywhere regular and predict a non-singular initial state for the Universe. Using that boundary condition, in certain particular cases the noboundary wave-function can be explicitly computed [2][3][4]. Another way by which one may compute the wave-function of the Universe is by directly solving the Wheeler-DeWitt equation [1]. The wave-function of the Universe for some important models have been computed using this approach [5][6][7][8][9][10].Several important theoretical results and predictions in quantum cosmology have been obtained with a negative cosmological constant [11], [12] and [3]. Besides that, we think it is important to understand more about such models which represent bound Universes (analogous to uni-dimensional atoms, in the present situation).In the present paper, we use the formalism of quantum cosmology in order to quantize a Friedmann-Robertson-Walker model in the presence of a negative cosmological constant and radiation. The radiation is treated by means of the variational formalism developed by Schutz [13]. The model has spatial sections with positive constant curvature. The wavefunction of the model satisfies a Wheeler-DeWitt equation, for the scale factor, which has the form of the Schrödinger's equation for the quartic anharmonic oscillator. We find the eigenvalues and eigenfunctions by using a method first developed by Chhajlany and Malnev. After that, we use the eigenfunctions in order to construct wave-packets for evaluating the time-dependent, expected value of the scale factor. We find that the expectatio...

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Notes on the quantization of FRW model in the presence of a cosmological constant and radiation

Monerat¹,

Silva²,

Oliveira‐Neto³

et al. 2005

Braz. J. Phys.

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“…However, there are also descriptions in which Dark Matter is unified with Dark Energy in a single constituent of the universe. One of these examples is the Chaplygin gas p g = −1/ρ g [37,38]. The use of the continuity equation leads to…”

Section: Alternative Descriptions Of the Acmmentioning

confidence: 99%

An extension of the cosmological standard model with a bounded Hubble expansion rate

Cortés

Induráin

2009

Astroparticle Physics

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The possibility of having an extension of the cosmological standard model with a Hubble expansion rate H constrained to a finite interval is considered. Two periods of accelerated expansion arise naturally when the Hubble expansion rate approaches to the two limiting values. The new description of the history of the universe is confronted with cosmological data and with several theoretical ideas going beyond the standard cosmological model.

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“…To find a solution to the above mentioned problems the straight and direct way could be the de Broglie-Bohm (dBB) interpretation of quantum cosmology. The dBB interpretation is favorable, especially for a quantum theory of cosmology, because this interpretation is able to resolve the conceptual problems of quantum cosmology [2]. However, we have a problem in using of this interpretation in quantum cosmology: It cannot describe the trajectories and non-zero velocities for real wave functions of quantum cosmology.…”

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confidence: 99%

Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

Fathi

Jalalzadeh

2017

Int J Theor Phys

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How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in [1]. In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.

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Quantum Cosmological Perfect Fluid Models

Cited by 176 publications

References 18 publications

Notes on the quantization of FRW model in the presence of a cosmological constant and radiation

Notes on the quantization of FRW model in the presence of a cosmological constant and radiation

An extension of the cosmological standard model with a bounded Hubble expansion rate

Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

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