Asymptotical AdS space from nonlinear gravitational models with stabilized extra dimensions

Günther, Uwe; Moniz, Paulo Vargas; Zhuk, Alexander

doi:10.1103/physrevd.66.044014

Cited by 24 publications

(12 citation statements)

References 41 publications

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“…3There are some other works about theoretical constructions of f ( R ) models based on quantum gravity, super-gravity and extra dimensional theories [341, 345, 537, 406, 163, 287, 288, 518, 519]. …”

mentioning

confidence: 99%

f(R) Theories

Felice

Tsujikawa

2010

Living Rev. Relativ.

3,670

3,400

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Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity — such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

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mentioning

confidence: 99%

f(R) Theories

Felice

Tsujikawa

2010

Living Rev. Relativ.

3,670

3,400

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“…There are some other works about theoretical constructions of f (R) models based on quantum gravity, supergravity and extra dimensional theories[341,345,537,406,163,287,288,518,519].…”

mentioning

confidence: 99%

f(R) theories

De Felice,

Tsujikawa

2010

Preprint

472

808

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Over the past decade, f (R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f (R) theories to cosmology and gravity -such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

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“…It is well known (see, e.g., [12,13]) that in the case of f (R) gravity, the Einstein equations take on the form…”

Section: Basic Equationsmentioning

confidence: 99%

“…It is indeed appealing to study models which combine both approaches, in other words, to consider nonlinear f (R) models in multidimensional space-time. As regards the cosmological aspects, such models were investigated in [12][13][14][15][16][17][18], where the authors focused mainly on the problems of internal space stabilization, early and late time accelerated expansion of the Universe and dark matter in the form of gravexcitons/radions. To be viable candidates, these models are required to satisfy the gravitational tests carried out in the Solar system, viz., the deflection of light, time delay of radar echoes and perihelion shift.…”

Section: Introductionmentioning

confidence: 99%

Effects of nonlinearity of f(R) gravity and perfect fluid in Kaluza–Klein models with spherical compactification

2020

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We study the effects associated with nonlinearity of f(R) gravity and of the background perfect fluid manifested in the Kaluza–Klein model with spherical compactification. The background space-time is perturbed by a massive gravitating source which is pressureless in the external space but has an arbitrary equation of state (EoS) parameter in the internal space. As characteristics of a nonlinear perfect fluid, the squared speeds of sound are not equal to the background EoS parameters in the external and internal spaces. In this setting, we find exact solutions to the linearized Einstein equations for the perturbed metric coefficients. For nonlinear models with $$f^{\prime \prime }(R_0)\ne 0$$f″(R0)≠0, we show that these coefficients acquire correction terms in the form of two summed Yukawa potentials and that in the degenerated case, the solutions are reduced to a single Yukawa potential with some “corrupted” prefactor (in front of the exponential function), which, in addition to the standard 1/r term, contains a contribution independent of the three-dimensional distance r. In the linear $$f''(R)=0$$f′′(R)=0 model, we generalize the previous studies to the case of an arbitrary nonlinear perfect fluid. We also investigate the particular case of the nonlinear background perfect fluid with zero speed of sound in the external space and demonstrate that a non-trivial solution exists only in the case of $$f''(R_0)=0$$f′′(R0)=0.

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Asymptotical AdS space from nonlinear gravitational models with stabilized extra dimensions

Cited by 24 publications

References 41 publications

f(R) Theories

f(R) Theories

f(R) theories

Effects of nonlinearity of f(R) gravity and perfect fluid in Kaluza–Klein models with spherical compactification

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