Quadratic quantum cosmology with Schutz' perfect fluid

Vakili, Babak

doi:10.1088/0264-9381/27/2/025008

Cited by 52 publications

(14 citation statements)

References 65 publications

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“…This Hamiltonian is very similar to the Hamiltonian obtained in the f (R) model presented in [41], except for the appearance of a new term −2 …”

Section: The Time Problem In the Quantum Cosmology Of The F (R T ) Gsupporting

confidence: 75%

“…There are various ways to do it [57], but in the following we choose a procedure that keeps the Hamiltonian Hermitian [41]. Hence we assume the following relations (we let P q = −i(∂/∂q)),…”

Section: The Wheeler-de Witt Equation In F (R T ) Gravitymentioning

confidence: 99%

“…One of the main obstacles in the understanding of quantum cosmology is the so-called problem of time, which comes from the Hamiltonian constraint in the Arnowitz-Deser-Misner (ADM) formalism, leading to the Wheeler-de Witt equation [38][39][40], a fundamental equation in canonical quantization of cosmology. The quantum cosmology of f (R) gravity theory with Schutz's fluid is discussed in [41,42], with new perspectives to the time problem in quantum gravity considered.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Cosmology of f(R, T) gravity

Harkó

Liang

2016

Eur. Phys. J. C

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Modified gravity theories have the potential of explaining the recent acceleration of the Universe without resorting to the mysterious concept of dark energy. In particular, it has been pointed out that matter-geometry coupling may be responsible for the recent cosmological dynamics of the Universe, and matter itself may play a more fundamental role in the description of the gravitational processes that usually assumed. In the present paper we study the quantum cosmology of the f (R, T ) theory of gravity, in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, and the trace of the matter energy-momentum tensor, respectively. For the background geometry we adopt the Friedmann-RobertsonWalker metric, and we assume that matter content of the Universe consists of a perfect fluid. In this framework we obtain the general form of the gravitational Hamiltonian, of the quantum potential, and of the canonical momenta, respectively. This allows us to formulate the full Wheeler-de Witt equation describing the quantum properties of this modified gravity model. As a specific application we consider in detail the quantum cosmology of the f (R, T ) = F 0 (R) + θ RT model, in which F 0 (R) is an arbitrary function of the Ricci scalar, and θ is a function of the scale factor only. The Hamiltonian form of the equations of motion, and the Wheeler-de Witt equations are obtained, and a time parameter for the corresponding dynamical system is identified, which allows one to formulate the Schrödinger-Wheeler-de Witt equation for the quantum-mechanical description of the model under consideration. A perturbative approach for the study of this equation is developed, and the energy levels of the Universe are obtained by using a twofold degenerate pera e-mail: 253659701@qq.com b e-mail: t.harko@ucl.ac.uk c e-mail: stslsd@mail.sysu.edu.cn turbation approach. A second quantization approach for the description of quantum time is also proposed and briefly discussed.

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“…This Hamiltonian is very similar to the Hamiltonian obtained in the f (R) model presented in [41], except for the appearance of a new term −2 …”

Section: The Time Problem In the Quantum Cosmology Of The F (R T ) Gsupporting

confidence: 75%

Section: The Wheeler-de Witt Equation In F (R T ) Gravitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Cosmology of f(R, T) gravity

Harkó

Liang

2016

Eur. Phys. J. C

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“…and modified gravity f (R) [22,23,24,25,26,27]. The Schutz's formalism is used even with success in anisotropic quantum cosmology [28,29,30,31,32,33,34], bouncing cosmologies [35,36,37] or very recently on Brans-Dicke theory and scalar-tensor theories [38,39,40,41].…”

Section: The Schutz's Formalism In Quantum Cosmologymentioning

confidence: 99%

Dynamics of a Perfect Fluid Through Velocity Potentials with Application in Quantum Cosmology

et al. 2016

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We review the Eulerian description of hydrodynamics using Seliger-Whitham's formalism (in classical case) and Schutz's formalism (in relativistic case). In these formalisms, the velocity field of a perfect fluid is described by scalar potentials.With this we can obtain the evolution equations of the fluid and its Hamiltonian.In the scenario of quantum cosmology the Schutz's formalism makes it possible to introduce phenomenologically a time variable in minisuperspace models.PACS number(s): 98.80.Cq, 98.80.Qc

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“…Here we can see that Rainbow function g 1 (E/E P ) do not take part in the Schrödinger-Wheeler-deWitt equation just like N. This can be seen as a scaling of the lapse function N by 1 g 1 (E/E P ) . In order to solve for the wave function Ψ we employ the separation of variables as Ψ(a, T ) = e −iET φ(a) (17) to get for flat case k = 0…”

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confidence: 99%

Quantum Rainbow Cosmological Model With Perfect Fluid

Majumder

2013

Int. J. Mod. Phys. D

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Isotropic quantum cosmological perfect fluid model is studied in the formalism of Rainbow gravity. It is found that the only surviving matter degree of freedom played the role of cosmic time. With the suitable choice of the Rainbow functions it is possible to find the wave packet naturally from the superposition of the wave functions of the Schrödinger-Wheeler-deWitt equation. The many-worlds interpretation of quantum mechanics is applied to investigate the behavior of the scale factor and the behavior is found to depend on the operator ordering. It is shown that the model in the Rainbow framework may avoid singularity yielding a bouncing non-singular universe.

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Quadratic quantum cosmology with Schutz' perfect fluid

Cited by 52 publications

References 65 publications

Quantum Cosmology of f(R, T) gravity

Quantum Cosmology of f(R, T) gravity

Dynamics of a Perfect Fluid Through Velocity Potentials with Application in Quantum Cosmology

Quantum Rainbow Cosmological Model With Perfect Fluid

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