Cosmological Models with Fractional Derivatives and Fractional Action Functional

Shchigolev, V. K.

doi:10.1088/0253-6102/56/2/34

Cited by 56 publications

(64 citation statements)

References 27 publications

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“…As well known, the fractional action cosmology (FAC) is the new field of research based on the principles and formalism of the fractional calculus applied to cosmology. In this paper, we present the results of study of some exact models in FAC constructed by the author on the basis of the fractional action functional in [1]. These models are followed from the fractional variational principle for the dynamical field theories in general and the theory of gravity formulated by El -Nabulsi (see, e.g., [2], [3] and references therein).…”

Section: Introductionmentioning

confidence: 99%

“…In the present work, we aim to develop further the FAC model proposed by the author in [1] and obtain the new exact solutions to this model. Exact solutions of the modified Friedmann equations in FAC are important to analyze the possible behavior of these models in aspect of the accelerated cosmological expansion in aspect of the recent observational data.…”

Section: Introductionmentioning

confidence: 99%

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Cosmic Evolution in Fractional Action Cosmology

Shchigolev¹

2013

DNC

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For the fractional action cosmological model, derived earlier by the author from the variational principle for a fractional action functional, the exact solutions are obtained. The case of a quasi - vacuum state of matter that fills the universe is considered. Moreover, on the basis of specific ansatz proposed in this paper for the cosmological term, the class of exact solutions of the model equations is obtained. Examples for some given laws of the cosmological term evolution are provided. Besides, a formula for the effective equation of state is derived, and the deceleration parameter of the obtained models is studied.Comment: 8 pages, 5 figures, fixed some typo

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cosmic Evolution in Fractional Action Cosmology

Shchigolev¹

2013

DNC

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“…• The ordinary time derivatives of the Friedmann equations of homogeneous and isotropic cosmology were replaced by fractional derivatives in [47][48][49][50]. In particular, in [50] it was shown that supernovae data on the late-time acceleration of the universe can be explained by fractional Friedmann equations with derivative order close to 3/2.…”

Section: (γ−1) Cmentioning

confidence: 99%

Classical and quantum gravity with fractional operators

Calcagni

2021

Preprint

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Following the same steps made for a scalar field in a parallel publication, we propose a class of perturbative theories of quantum gravity based on fractional operators, where the kinetic operator of the graviton is either made of fractional derivatives or a covariant fractional d'Alembertian. The classical action for each theory is constructed and the equations of motion are derived. Unitarity and renormalizability of theories with a fractional d'Alembertian are also considered. We argue that unitarity and power-counting renormalizability never coexist, although in some cases one-loop unitary and finiteness are possible. One of the theories is unitary and infrared-finite and can serve as a ghost-free model with large-scale modifications of general relativity.

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“…Recently, a class of phenomenological models based on the concept of fractional calculus of variations, which is called the fractional action cosmology (FAC) has been proposed by El-Nabulsi [20]- [23]. Later, we significantly improved and developed these models in our works [24] - [26]. Our models are built on the…”

Section: Introductionmentioning

confidence: 99%

Fractional action cosmology with an effective \(\wedge\) -term

Shchigolev

2016

IJAA

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We continue studying the cosmological models derived from the fractional variational principle applied to the gravitational sector of the action functional. Within the frame of these models, the effective cosmological term could arise as a result of the non-zero Hubble parameter. At the same time, the continuity equation for the matter remains unchanged in its standard form. In this work, we are going to obtain some exact solutions for our model originating from the several kinematic assumptions. At that, we find the main cosmography parameters of the model and the corresponding equations of state of matter that fills the universe se. First, we proceed from an initially given law of evolution of the universe in some standard scenarios. Then, several exact solutions are obtained from the proposed earlier evolutionary laws for the effective cosmological term.

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Cosmological Models with Fractional Derivatives and Fractional Action Functional

Abstract: Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both cases is given.

Cited by 56 publications

References 27 publications

Cosmic Evolution in Fractional Action Cosmology

Cosmic Evolution in Fractional Action Cosmology

Classical and quantum gravity with fractional operators

Fractional action cosmology with an effective \(\wedge\) -term

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