Quantum mechanics and geodesic deviation in the brane world

Rasouli, S. M. M.; Bahrehbakhsh, Amir F.; Jalalzadeh, S.; Farhoudi, Mehrdad

doi:10.1209/0295-5075/87/40006

Cited by 10 publications

(6 citation statements)

References 26 publications

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“…where c 3 is a constant. 9 In order to obtain exact solutions for the field equations, we first obtain the differential equation for the scale factor only: (i) We substitute p φ and p from relations (19) and (136) into equation (27). Then, using (139) and (144), we obtain…”

Section: Gde For Null Vector Field In the Context Of The Mbdtmentioning

confidence: 99%

“…The GDE with the Friedmann-Lemaître-Robertson-Walker (FLRW) background has been studied in the Brans-Dicke-Rastall framework [8]. In [9], by considering the induced GDE in the brane world models, it has been shown that proper time of test particle can be related to the integral multiples of a fundamental Compton-type unit of length. In [10], the GDE has been studied in the context of the f (T ) gravity.…”

Section: Introductionmentioning

confidence: 99%

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Modified Brans–Dicke theory in arbitrary dimensions

Rasouli

Farhoudi

Moniz

2014

Class. Quantum Grav.

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Within an algebraic framework, used to construct the induced-matter-theory (IMT) setting, in (D + 1)-dimensional Brans-Dicke (BD) scenario, we obtain a modified BD theory (MBDT) in D dimensions. Being more specific, from the (D + 1)-dimensional field equations, a D-dimensional BD theory, bearing new features, is extracted by means of a suitable dimensional reduction onto a hypersurface orthogonal to the extra dimension. In particular, the BD scalar field in such Ddimensional theory has a self-interacting potential, which can be suitably interpreted as produced by the extra dimension. Subsequently, as an application to cosmology, we consider an extended spatially flat FLRW geometry in a (D + 1)-dimensional space-time. After obtaining the power-law solutions in the bulk, we proceed to construct the corresponding physics, by means of the induced MBDT procedure, on the D-dimensional hypersurface. We then contrast the resulted solutions (for different phases of the universe) with those usually extracted from the conventional GR and BD theories in view of current ranges for cosmological parameters. We show that the induced perfect fluid background and the induced scalar potential can be employed, within some limits, for describing different epochs of the universe. Finally, we comment on the observational viability of such a model.

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Section: Gde For Null Vector Field In the Context Of The Mbdtmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modified Brans–Dicke theory in arbitrary dimensions

Rasouli

Farhoudi

Moniz

2014

Class. Quantum Grav.

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“…The geodesic deviation (GD) equation is a pertinent tool to study properties of curved spacetimes [17,18,19,20]. It has been extensively investigated within different gravitational theories, by means of various exact cosmological solutions (see, e.g., [21,22,23,24,25] and references therein). Therefore, we establish the GD formalism associated with the SB and MSBT alike [4,16].…”

Section: Introductionmentioning

confidence: 99%

Geodesic deviation in Saez-Ballester theory

Rasouli,

Sakellariadou,

Moniz

2022

Preprint

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We study the geodesic deviation (GD) equation in a generalized version of the Sáez-Ballester (SB) theory in arbitrary dimensions. We first establish a general formalism and then restrict to particular cases, where (i) the matter-energy distribution is that of a perfect fluid, and (ii) the spacetime geometry is described by a vanishing Weyl tensor. Furthermore, we consider the spatially flat FLRW universe as the background geometry. Based on this setup, we compute the GD equation as well as the convergence condition associated with fundamental observers and past directed null vector fields. Moreover, we extend that framework and extract the corresponding geodesic deviation in the modified Sáez-Ballester theory (MSBT), where the energy-momentum tensor and potential emerge strictly from the geometry of the extra dimensions. In order to examine our herein GD equations, we consider two novel cosmological models within the SB framework. Moreover, we discuss a few quintessential models and a suitable phantom dark energy scenario within the mentioned SB and MSBT frameworks. Noticing that our herein cosmological models can suitably include the present time of our Universe, we solve the GD equations analytically and/or numerically. By employing the correct energy conditions plus recent observational data, we consistently depict the behavior of the deviation vector η(z) and the observer area distance r 0 (z) for our models. Concerning the Hubble constant problem, we specifically focus on the observational data reported by the Planck collaboration and the SH0ES collaboration to depict η(z) and r 0 (z) for our herein phantom model. Subsequently, we contrast our results with those associated with the ΛCDM model. We argue that the MSBT can be considered as a fitting candidate for a proper description of the late evolution of the universe.

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“…Wesson [23] has also derived a form of the Heisenberg relation that applies to real and virtual particles using five-dimensional IMT. (For an extension of this idea to brane gravity, please see [24].) In this regard, the authors of [25] derived the induced Einstein equation on the perturbed brane by contracting the Gauss-Codazzi equations.…”

Section: Introductionmentioning

confidence: 99%

Noncompactified Kaluza–Klein Gravity

2022

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We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space–Time–Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans–Dicke theory and the modified Sáez–Ballester theory are briefly explained. Finally, we apply the latter to the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological models in arbitrary dimensions and analyze the corresponding solutions.

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Quantum mechanics and geodesic deviation in the brane world

Cited by 10 publications

References 26 publications

Modified Brans–Dicke theory in arbitrary dimensions

Modified Brans–Dicke theory in arbitrary dimensions

Geodesic deviation in Saez-Ballester theory

Noncompactified Kaluza–Klein Gravity

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