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

Khosravi, Nima; Sepangi, H. R.; Vakili, Babak

doi:10.1007/s10714-009-0894-7

Cited by 9 publications

(7 citation statements)

References 62 publications

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“…It is seen from this figure that the wave function has a well-defined behavior near a = 0 and describes a universe emerging out of nothing without any tunneling. Now to see that how the quantum solutions may describe an expanding or contracting universe, we use a mechanism which we have called the probabilistic evolutionary process (PEP), based on the probabilistic structure of quantum systems, to provide a sense of the evolution embedded in the wave function of the universe (see [14] for details). This is based on the fact that in quantum systems the square of a state defines the probability, P a = |Ψ(a)| 2 .…”

Section: Quantum Modelmentioning

confidence: 99%

Classical and quantum Hořava–Lifshitz cosmology in a minisuperspace perspective

Vakili

Kord

2013

Gen Relativ Gravit

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We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology in the framework of the gravity theory proposed by Hořava, the so-called Hořava-Lifshitz theory of gravity. Beginning with the ADM representation of the action corresponding to this model, we construct the Lagrangian in terms of the minisuperspace variables and show that in comparison with the usual Einstein-Hilbert gravity, there are some correction terms coming from the Hořava theory. Either in the matter free or in the case when the considered universe is filled with a perfect fluid, the exact solutions to the classical field equations are obtained for the flat, closed and open FRW model and some discussions about their possible singularities are presented. We then deal with the quantization of the model in the context of the Wheeler-DeWitt approach of quantum cosmology to find the cosmological wave function. We use the resulting wave functions to investigate the possibility of the avoidance of classical singularities due to quantum effects.

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Section: Quantum Modelmentioning

confidence: 99%

Classical and quantum Hořava–Lifshitz cosmology in a minisuperspace perspective

Vakili

Kord

2013

Gen Relativ Gravit

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“…In fact, introducing relations such as (A1), that can be seen in many investigations [see e.g. [83][60]], may just be an appropriate mathematical transformation, at least in our paper, to derive the equations of motion with a simpler manner. We should stress that the only way to recover the standard (commutative) results from the noncommutative ones is to set the deformation parameter equal to zero.…”

Section: (A1)mentioning

confidence: 99%

Gravitational collapse of a homogeneous scalar field in deformed phase space

et al. 2014

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We study the gravitational collapse of a homogeneous scalar field, minimally coupled to gravity, in the presence of a particular type of dynamical deformation between the canonical momenta of the scale factor and of the scalar field. In the absence of such a deformation, a class of solutions can be found in the literature [R. Goswami and P. S. Joshi, arXiv:gr-qc/0410144], whereby a curvature singularity occurs at the collapse end state, which can be either hidden behind a horizon or be visible to external observers. However, when the phase-space is deformed, as implemented herein this paper, we find that the singularity may be either removed or instead, attained faster. More precisely, for negative values of the deformation parameter, we identify the emergence of a negative pressure term, which slows down the collapse so that the singularity is replaced with a bounce. In this respect, the formation of a dynamical horizon can be avoided depending on the suitable choice of the boundary surface of the star. Whereas for positive values, the pressure that originates from the deformation effects assists the collapse toward the singularity formation. In this case, since the collapse speed is unbounded, the condition on the horizon formation is always satisfied and furthermore the dynamical horizon develops earlier than when the phase-space deformations are absent. These results are obtained by means of a thoroughly numerical discussion.

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“…We start by introducing the Einstein-Hilbert action in a Cartesian coordinate [5][6] ds N c dt a dx dy dz (9) where N N t is the lapse function. Subsequently, the Ricci scalar and determinant of metric (9) (10) 2 6 g N a…”

Section: A Spatially Flat Cosmological Modelmentioning

confidence: 99%

“…and p w (6) where n is a constant. For different type of mass-energy, the value of n as well as w would be different.…”

Section: Introductionmentioning

confidence: 99%

Friedmann equation with quantum potential

Siong

Radiman

Nikouravan

2013

AIP Conference Proceedings

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Abstract. Friedmann equations are used to describe the evolution of the universe. Solving Friedmann equations for the scale factor indicates that the universe starts from an initial singularity where all the physical laws break down. However, the Friedmann equations are well describing the late-time or large scale universe. Hence now, many physicists try to find an alternative theory to avoid this initial singularity. In this paper, we generate a version of first Friedmann equation which is added with an additional term. This additional term contains the quantum potential energy which is believed to play an important role at small scale. However, it will gradually become negligible when the universe evolves to large scale.

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

Cited by 9 publications

References 62 publications

Classical and quantum Hořava–Lifshitz cosmology in a minisuperspace perspective

Classical and quantum Hořava–Lifshitz cosmology in a minisuperspace perspective

Gravitational collapse of a homogeneous scalar field in deformed phase space

Friedmann equation with quantum potential

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