Multi-dimensional classical and quantum cosmology: exact solutions, signature transition and stabilization

A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these problems find natural solutions in a universe described by an increasing time parameter. PACS: 04.50.+h, 02.40.Gh, 11.25.Mj IntroductionNon-commutativity between space-time coordinates, first introduced in [1], has been attracting considerable attention in the recent past [2,3,4]. This renewed interest has its roots in the development of string and M-theories, [5,6]. However, in all fairness, investigation of non-commutative theories may also be justified in its own right because of the interesting predictions regarding, for example, the IR/UV mixing and non-locality [7], Lorentz violation [8] and new physics at very short distance scales [9,10,11]. The impact of non-commutativity in cosmology has also been considerable and has been addressed in different works [12]. Hopefully, non-commutative cosmology would lead us to the formulation of semiclassical approximations of quantum gravity and tackles the cosmological constant problem [13]. Of particular interest would be the application of non-commutativity to multi-dimensional cosmology.Multi-dimensional spaces were introduced for the geometric unification of interactions by Kaluza and Klein and have since been a source of inspiration for numerous authors [14]. Also, the introduction of extra dimensions suggests possible solutions to some of the important problems that cosmology has been facing, namely, the mass hierarchy and cosmological constant problem, to name but a few. That said, it should also be mentioned that the question of compactification and the stabilization of the extra dimensions is a challenge one cannot avoid. In this paper, we have considered a multidimensional cosmology with a cosmological constant and introduced non-commutativity between the scale factors of our ordinary space and the extra dimensions. We have shown that the classical cosmology of this model can be solved exactly. These solutions offer an explanation for the cosmological constant problem and show how the extra dimensions can be compactified. *

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“…Using the above transformations introduced in [15] and concentrating on k = 0, the Lagrangian becomes…”

Section: The Modelmentioning

confidence: 99%

Non-commutative multi-dimensional cosmology

Khosravi¹,

Jalalzadeh²,

Sepangi³

2006

J. High Energy Phys.

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“…This phenomenon has been studied at the classical and quantum cosmology level by other authors, see for example [8], [9] and [10]. There are a number of works which support the idea that signature transition would provide a mechanism for compactification in higher dimensional cosmology [11,12,13,14]. In [11] a higher dimensional FRW model with a positive cosmological constant was considered with topology S 3 × S 6 as the spatial section and two scale factors a 1 and a 2 .…”

Section: Introdutionmentioning

confidence: 98%

Compactification and signature transition in Kaluza–Klein spinor cosmology

2006

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We study the classical and quantum cosmology of a 4 + 1-dimensional space-time with a nonzero cosmological constant coupled to a self interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor R(t) and an internal scale factor a(t) associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition from a Euclidean to a Lorentzian domain. Such transitions suggest a compactification mechanism for the internal and external scale factors such that a ∼ R −1 in the Lorentzian region. The corresponding quantum cosmology and the ensuing Wheeler-DeWitt equation have exact solutions in the mini-superspace when the spinor field is free, leading to wavepackets undergoing signature change. The question of stabilization of the extra dimension is also discussed.

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“…We have used this concept to construct our higher dimensional traversable wormhole. First, we consider dynamical compactification as the evolution of the fifth dimension [39,40]. This assumption will ensure that the extra dimension remains compact and non-observable within the growth of the normal dimensions.…”

Section: Introductionmentioning

confidence: 99%

Five dimensional cosmological traversable wormhole

2015

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In this paper, a traversable wormhole in the Friedmann-Lemaître-Robertson-Walker (FLRW) model with one extra spacelike compact dimension is studied. We have chosen dynamical compactification as the evolution of the fifth dimension. In this respect, we study how the existence of the extra dimension, affect the behavior of the energy density, the shape function and the scale factor. It is shown that the total matter can be non-exotic and the violation of the weak energy condition can be avoided.

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Multi-dimensional classical and quantum cosmology: exact solutions, signature transition and stabilization

Cited by 22 publications

References 25 publications

Non-commutative multi-dimensional cosmology

Non-commutative multi-dimensional cosmology

Compactification and signature transition in Kaluza–Klein spinor cosmology

Five dimensional cosmological traversable wormhole

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