Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative

Torres, Isaac; Fabris, J. C.; Piattella, Oliver F.; Batista, A. B.

doi:10.3390/universe6040050

Cited by 19 publications

(13 citation statements)

References 53 publications

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“…13 Endeavouring towards cosmology (including in a quantum mechanical context) has also recently emerged. [43][44][45] In the review paper herein presented, we follow the 'ouverture' made in another publication, with an emphasis on the canonical description. 45 After a summary of FQM, we presented a new solution for a FRW model, within the scope of time-FQM for a Schrödinger-Wheeler-DeWitt equation.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…Namely, fractional quantum cosmology (FQC). It has been emerging gradually, [43][44][45] subsequently pointing to fascinating opportunities and 'lateral' connections with what were unforeseen mathematics and physics domains, with this review herewith following a particular (canonical) route as charted in another publication. 45 Before proceeding, let us point that this review paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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Broadening quantum cosmology with a fractional whirl

Rasouli,

Jalalzadeh,

Moniz

2021

Preprint

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We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically, we investigate and then discuss a model of stiff matter in a spatially flat homogeneous and isotropic universe. A new quantum cosmological solution, where fractional calculus implications are explicit, is presented and then contrasted with the corresponding standard quantum cosmology setting.

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Section: Discussion and Outlookmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Broadening quantum cosmology with a fractional whirl

Rasouli,

Jalalzadeh,

Moniz

2021

Preprint

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“…A significantly different approach to the application of fractional derivatives in cosmology from the above approach is presented in Ref. [99] , where quantization is studied in terms of the fractional derivative of the cosmological coupling theory of the non-minimal derivative, namely, the Fab Four John theory. Its Hamiltonian version is the problem of fractional powers of momenta.…”

Section: Some Recent Studies Of Facmentioning

confidence: 99%

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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“…The term G µν ∇ µ φ∇ ν φ is also present in the so-called Fab Four theory [6]. Just to mention some of the studies about that kind of couplings, see [7][8][9][10][11][12][13][14], for instance.…”

Section: Introductionmentioning

confidence: 99%

Gravitational Waves Constraint over Asymptotic Inflation in a Nonminimal Derivative Coupling Cosmology

Torres¹,

Santos²

2022

Preprint

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In this paper, we review the nonminimal derivative coupling (NDC) between gravity and a scalar field, from the point of view of the constraint imposed by the detection of gravitational waves. We study in detail the relation between the asymptotic inflationary solution obtained from NDC and its relation with the constraint, by means of a dynamical system analysis, with tow different sets of variables: the orinal ones and new variables that allow us to study asymptotic limits as points in phase space. In this sense, we thus show that the asymptotic inflationary solutions from NDC are incompatible with the gravitational waves speed constraint.

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Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative

Cited by 19 publications

References 53 publications

Broadening quantum cosmology with a fractional whirl

Broadening quantum cosmology with a fractional whirl

Fractional-order derivatives in cosmological models of accelerated expansion

Gravitational Waves Constraint over Asymptotic Inflation in a Nonminimal Derivative Coupling Cosmology

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