New Metrics from a Fractional Gravitational Field

El-Nabulsi, Rami Ahmad

doi:10.1088/0253-6102/68/3/309

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…It is also possible to arrive at a similar situation in the weak field if the higher dimensional spacetime is assumed to be fractal in nature. However as demonstrated in [32], in order to arrive at a 1/r gravitational potential it was necessary to work in five dimensions with some particular choices related to the fractal structure of the spacetime (see also [33][34][35][36]). However, the scenario we are interested in is completely different conceptually, as the spacetime manifold in consideration does not posses any fractal structure and the solution is derived from the fully non-linear theory in a series of spacetime dimensions.…”

Section: Introductionmentioning

confidence: 99%

1/r potential in higher dimensions

Chakraborty

Dadhich

2018

Eur. Phys. J. C

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In Einstein gravity, gravitational potential goes as 1/r d−3 in d non-compactified spacetime dimensions, which assumes the familiar 1/r form in four dimensions. On the other hand, it goes as 1/r α , with α = (d −2m −1)/m, in pure Lovelock gravity involving only one mth order term of the Lovelock polynomial in the gravitational action. The latter offers a novel possibility of having 1/r potential for the noncompactified dimension spectrum given by d = 3m+1. Thus it turns out that in the two prototype gravitational settings of isolated objects, like black holes and the universe as a whole -cosmological models, the Einstein gravity in four and mth order pure Lovelock gravity in 3m + 1 dimensions behave in a similar fashion as far as gravitational interactions are considered. However propagation of gravitational waves (or the number of degrees of freedom) does indeed serve as a discriminator because it has two polarizations only in four dimensions.

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Section: Introductionmentioning

confidence: 99%

1/r potential in higher dimensions

Chakraborty

Dadhich

2018

Eur. Phys. J. C

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“…The same remarks could be address to Ref. [72],in which the modified cosmological equations are obtained using the periodic weight function g t (τ ) in the generalized action (25) as follows:…”

Section: The Recent Studies In Fractional Derivatives Gravity and Cos...mentioning

confidence: 87%

“…Similarly to Refs. [71,72] , the number of fractional action cosmological models are considered in articles [73]- [76], where the models are followed again from the fractional action applied to the classical Lagrangian of a curve defined by L = (1/2)g ij ẋi ẋj , where g ij is the metric tensor. The modified Friedmann equations are used in the form:…”

Section: The Recent Studies In Fractional Derivatives Gravity and Cos...mentioning

confidence: 99%

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Fractional-order derivatives in cosmological models of accelerated expansion

Shchigolev

2021

Preprint

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In this brief review, we present the results of the fractional differential approach in cosmology in the context of the exact models of cosmological accelerated expansion obtained by several authors to date. Most of these studies are devoted to the problem of introducing fractional derivatives or fractional integrals into the classical General Relativity (GR). There are several observational and theoretical motivations to investigate the modified or alternative theories of GR. Among other things, we cover General Relativity modified by a phenomenological approach dealing with fractional calculus. At the same time, a sufficiently large number of exact solutions of the cosmological equations modified by this approach were obtained. Some of these models may be especially relevant in the light of solving the problem of late accelerated expansion of the universe. These studies are largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

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“…Additionally, fractional calculus has been utilized in investigating phantom cosmology with conformal coupling [67], Ornstein-Uhlenbeck-like fractional differential equations in cosmology [68], fractional action cosmology with a variable-order parameter [69], and wormholes in fractional action cosmology [70]. Notably, new metrics have been considered [71], while the application of fractional calculus has also extended to the study of dark energy models in emergent, logamediate, and intermediate scenarios of the universe [72,73]. As an example, the work of [50,52] yielded a value of α = 0.926 for the order of the Riemann-Liouville fractional integral, providing further insights into the intricacies of the field.…”

Section: Introductionmentioning

confidence: 99%

Estimated Age of the Universe in Fractional Cosmology

Costa,

Jalalzadeh,

da Silva Júnior

et al. 2023

Fractal Fract

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Our proposed cosmological framework, which is based on fractional quantum cosmology, aims to address the issue of synchronicity in the age of the universe. To achieve this, we have developed a new fractional ΛCDM cosmological model. We obtained the necessary formalism by obtaining the fractional Hamiltonian constraint in a general minisuperspace. This formalism has allowed us to derive the fractional Friedmann and Raychaudhuri equations for a homogeneous and isotropic cosmology. Unlike the traditional de Sitter phase, our model exhibits a power-law accelerated expansion in the late-time universe, when vacuum energy becomes dominant. By fitting the model’s parameters to cosmological observations, we determined that the fractional parameter of Lévy equals α=1.986. Additionally, we have calculated the age of the universe to be 13.8196 Gyr. Furthermore, we have found that the ratio of the age to Hubble time from the present epoch to the distant future is finite and confined within the interval 0.9858≤Ht<95.238.

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New Metrics from a Fractional Gravitational Field

Cited by 9 publications

References 26 publications

1/r potential in higher dimensions

1/r potential in higher dimensions

Fractional-order derivatives in cosmological models of accelerated expansion

Estimated Age of the Universe in Fractional Cosmology

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