Modified Brans–Dicke theory of gravity from five-dimensional vacuum

Aguilar, José Edgar Madriz; Romero, C.; Barros, A.

doi:10.1007/s10714-007-0517-0

Cited by 25 publications

(46 citation statements)

References 30 publications

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“…Generalizations of Kaluza-Klein theory present themselves as a suitable scheme to frame modern cosmological observations. In fact, after SNIe observations, several attempts have been made to match induced-matter theories with the dark-energy puzzle [47][48][49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

Troisi

2017

Eur. Phys. J. C

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Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energymomentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological fourdimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Fivedimensional f (R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f (R) = f 0 R n the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions.

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Section: Introductionmentioning

confidence: 99%

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

Troisi

2017

Eur. Phys. J. C

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“…In this approach, some features of a 5D vacuum Brans-Dicke (BD) theory based on the idea of IM theory have recently been demonstrated [24], in where the role of GR as fundamental underlying theory has been replaced by the BD theory of gravitation. Actually, it has been shown that 5D vacuum BD equations, when reduced to four dimensions, lead to a modified version of the 4D Brans-Dicke theory which includes an induced potential.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, some misleading statements and equations have been asserted in Ref. [24], and hence we have re-derived the procedure in Sect. 2.…”

Section: Introductionmentioning

confidence: 99%

“…In the next section, we give a brief review of the induced modified BD theory from a 5D vacuum space-time to rederive the induced energy-momentum tensor, as has been introduced in Ref. [24], for our purpose to employ the energy density and pressure. In Sect.…”

Section: Introductionmentioning

confidence: 99%

“…This equivalency can be viewed as the main point within this work which distinguishes it from Refs. [24][25][26]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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FRW cosmology from five dimensional vacuum Brans–Dicke theory

2010

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We follow the approach of induced-matter theory for a five-dimensional (5D) vacuum Brans-Dicke theory and introduce induced-matter and induced potential in four dimensional (4D) hypersurfaces, and then employ a generalized FRW type solution. We confine ourselves to the scalar field and scale factors be functions of the cosmic time. This makes the induced potential, by its definition, vanishes, but the model is capable to expose variety of states for the universe. In general situations, in which the scale factor of the fifth dimension and scalar field are not constants, the 5D equations, for any kind of geometry, admit a power-law relation between the scalar field and scale factor of the fifth dimension. Hence, the procedure exhibits that 5D vacuum FRW-like equations are equivalent, in general, to the corresponding 4D vacuum ones with the same spatial scale factor but a new scalar field and a new coupling constant,ω. We show that the 5D vacuum FRW-like equations, or its equivalent 4D vacuum ones, admit accelerated solutions. For a constant scalar field, the equations reduce to the usual FRW equations with a typical radiation dominated universe. For this situation, we obtain dynamics of scale factors of the ordinary and extra dimensions for any kind of geometry without any priori assumption among them. For nonconstant scalar fields and spatially flat geometries, solutions are found to be in the form of power-law and exponential ones. We also employ the weak energy condition for the induced-matter, that gives two constraints with negative or positive pressures. All types of solutions fulfill the weak energy condition in different ranges. The 123 848 A. F. Bahrehbakhsh et al.power-law solutions with either negative or positive pressures admit both decelerating and accelerating ones. Some solutions accept a shrinking extra dimension. By considering non-ghost scalar fields and appealing the recent observational measurements, the solutions are more restricted. We illustrate that the accelerating power-law solutions, which satisfy the weak energy condition and have non-ghost scalar fields, are compatible with the recent observations in ranges −4/3 < ω ≤ −1.3151 for the coupling constant and 1.5208 ≤ n < 1.9583 for dependence of the fifth dimension scale factor with the usual scale factor. These ranges also fulfill the conditionω > −3/2 which prevents ghost scalar fields in the equivalent 4D vacuum Brans-Dicke equations. The results are presented in a few tables and figures.

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Energy conditions in a modified Brans-Dicke theory

Amani

Halpern²

2022

Gen Relativ Gravit

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Modified Brans–Dicke theory of gravity from five-dimensional vacuum

Cited by 25 publications

References 30 publications

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

FRW cosmology from five dimensional vacuum Brans–Dicke theory

Energy conditions in a modified Brans-Dicke theory

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