Generalized Uncertainty Principle in Astrophysics from Fermi Statistical Physics Arguments

El-Nabulsi, Rami Ahmad

doi:10.1007/s10773-020-04480-7

Cited by 17 publications

(5 citation statements)

References 23 publications

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“…In Refs. [93,94], the FRW cosmology characterized by a scale factor obeying different independent types of fractional differential equations was studied, and both types of fractional operators: the Riemann-Liouville fractional integral and the Caputo fractional derivative were considered. The solutions for such models are given in terms of Mittag-Leffler and generalized Kilbas-Saigo-Mittag-Leffler functions.…”

Section: Some Recent Studies Of Facmentioning

confidence: 99%

Fractional-order derivatives in cosmological models of accelerated expansion

Shchigolev

2021

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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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Section: Some Recent Studies Of Facmentioning

confidence: 99%

Fractional-order derivatives in cosmological models of accelerated expansion

Shchigolev

2021

Preprint

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“…Since the earliest days of the development of the theory [31], the minimum length concept is a hallmark of quantum gravity [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. In fact, it suffices to combine arguments from general relativity and quantum mechanics to arrive at fundamental and absolute limitations to measurements [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. This effect can be modelled easily within nonrelativistic quantum mechanics through modifications to the algebra of observables [64][65][66][67][68], resulting in generalized uncertainty principles (GUPs).…”

Section: Introductionmentioning

confidence: 99%

Towards quantum Mechanics on the curved cotangent bundle

Wagner¹

2021

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The minimum length paradigm, a cornerstone of quantum gravity phenomenology, and quantum theories on nontrivial momentum space have been brought into explicit correspondence, recently. However, owing to the fact that coordinate transformations introduce additional positiondependence to the otherwise solely momentum-dependent metric, there is no fully consistent formulation of these theories beyond Cartesian coordinates and, in particular, no position representation. This paper is intended to take the first steps in bridging this gap by promoting the measure of the Hilbert space scalar product to an operator and merging it, by analogy with geometric quantization, with the wave functions. Correspondingly, we find a natural action of the position and momentum operators on the resulting wave densities in both of their representations, as well as the free particle-Hamiltonian and the geodesic distance. These reduce to their counterparts in DeWitt's approach to quantum mechanics on curved spaces in the corresponding circumstances. We apply the formalism perturbatively in a Riemann normal coordinate-like expansion, with curvature in position and momentum space simultaneously, to the isotropic harmonic oscillator and the hydrogen-like atom. Interestingly, under suitable choice of operator ordering, the former retains its symmetry with respect to exchange of positions and momenta, making it impossible to distinguish positionfrom momentum space-curvature. We thus obtain a true instantiation of Born reciprocity on the curved cotangent bundle.

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“…[78,79] and El-Nabulsi [75][76][77]. Moreover, in cosmology the NSL are used for describing dark energy and dark matter [38,[80][81][82][83].…”

Section: Introductionmentioning

confidence: 99%