Fractional-order derivatives in cosmological models of accelerated expansion

First Time ◽

Reference Tool

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.

Minimal extension of General Relativity: Alternative gravity model with non-minimal coupling between matter and curvature

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887814600032 ◽

2014 ◽

Vol 11 (02) ◽

pp. 1460003 ◽

Cited By ~ 14

Author(s):

Orfeu Bertolami ◽

Jorge Páramos

Keyword(s):

General Relativity ◽

Lagrangian Density ◽

Density Fluctuations ◽

Accelerated Expansion ◽

Minimal Extension ◽

Minimal Coupling ◽

Scalar Theories ◽

The Impact ◽

We examine an extension of General Relativity with an explicit non-minimal coupling between matter and curvature. The purpose of this work is to present an overview of the implications of the latter to various contexts, ranging from astrophysical matter distributions to a cosmological setting. Various results are discussed, including the impact of this non-minimal coupling on the choice of Lagrangian density, on a mechanism to mimic galactic and cluster dark matter, on the possibility of accounting for the accelerated expansion of the Universe, energy density fluctuations and modifications to post-inflationary reheating. The equivalence between a model exhibiting a non-minimal coupling and multi-scalar-theories is also discussed.

DELTA GRAVITY AND THE ACCELERATED EXPANSION OF THE UNIVERSE

International Journal of Modern Physics E ◽

10.1142/s0218301311040086 ◽

2011 ◽

Vol 20 (supp01) ◽

pp. 65-72

Author(s):

JORGE ALFARO

Keyword(s):

General Relativity ◽

Gravitational Field ◽

Cosmological Constant ◽

Equivalence Principle ◽

Equations Of Motion ◽

Accelerated Expansion ◽

Symmetric Tensors ◽

Test Particles ◽

We study a model of the gravitational field based on two symmetric tensors. The equations of motion of test particles are derived. We explain how the Equivalence principle is recovered. Outside matter, the predictions of the model coincide exactly with General Relativity, so all classical tests are satisfied. In Cosmology, we get accelerated expansion without a cosmological constant.

General relativity and the accelerated expansion of the universe

Resonance ◽

10.1007/s12045-012-0024-9 ◽

2012 ◽

Vol 17 (3) ◽

pp. 254-273

Author(s):

Patrick Das Gupta

Keyword(s):

General Relativity ◽

Accelerated Expansion ◽

Kinetic studies relating to the accelerated expansion of the Universe

10.21203/rs.3.rs-777944/v1 ◽

2021 ◽

Author(s):

Wei Zhang ◽

Cheng Deng

Keyword(s):

General Relativity ◽

Hubble Constant ◽

Kinetic Studies ◽

Physical Significance ◽

Accelerated Expansion ◽

Newtonian Mechanics ◽

Accelerating Expansion ◽

The Masses ◽

Abstract After taking into account the mass loss of galaxies and stars at the cosmic scale, the speed and acceleration of the accelerating expansion of the Universe are derived from general relativity and Newtonian mechanics, as respectively. The physical significance of the Hubble constant is proved to be the average of the masses ejected per second per unit mass in the observed range, and it is shown that the accelerated expansion of the universe doesn’t require dark energy

Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe

Publications of the Astronomical Society of Australia ◽

10.1071/as03040 ◽

2004 ◽

Vol 21 (1) ◽

pp. 97-109 ◽

Cited By ~ 97

Author(s):

Tamara M. Davis ◽

Charles H. Lineweaver

Keyword(s):

General Relativity ◽

Confidence Level ◽

Speed Of Light ◽

Observable Universe ◽

Superluminal Expansion ◽

The Universe ◽

Recession Velocity ◽

Common Misconceptions ◽

Rule Out

AbstractWe use standard general relativity to illustrate and clarify several common misconceptions about the expansion of the universe. To show the abundance of these misconceptions we cite numerous misleading, or easily misinterpreted, statements in the literature. In the context of the new standard ΛCDM cosmology we point out confusions regarding the particle horizon, the event horizon, the ‘observable universe’ and the Hubble sphere (distance at which recession velocity = c). We show that we can observe galaxies that have, and always have had, recession velocities greater than the speed of light. We explain why this does not violate special relativity and we link these concepts to observational tests. Attempts to restrict recession velocities to less than the speed of light require a special relativistic interpretation of cosmological redshifts. We analyze apparent magnitudes of supernovae and observationally rule out the special relativistic Doppler interpretation of cosmological redshifts at a confidence level of 23σ.

The influence of the dark energy model in the Roche potential for interacting galaxies

Izvestiya vysshikh uchebnykh zavedenii. Fizika ◽

10.17223/00213411/63/11/127 ◽

2020 ◽

pp. 127-130

Author(s):

U.N. Zakirov ◽

Keyword(s):

Dark Energy ◽

Equivalence Principle ◽

Dark Energy Model ◽

Energy Model ◽

Interacting Galaxies ◽

Vacuum Field ◽

Accelerated Expansion ◽

First Time ◽

For the first time, the influence of the dark energy model - a new non-vacuum field - in the generalized (with allowance for the equivalence principle) Roche potential for interacting galaxies was considered. The equation of thermodynamics of the mentioned field and its possible evolutions affecting on the accelerated expansion of the Universe is given.

Cosmological constant

10.1093/oso/9780198802877.003.0026 ◽

2018 ◽

Author(s):

Michael Kachelriess

Keyword(s):

Dark Energy ◽

Cosmological Constant ◽

Accelerated Expansion ◽

Vacuum Fluctuations ◽

Present Epoch ◽

Modify Gravity ◽

The contribution of vacuum fluctuations to the cosmological constant is reconsidered studying the dependence on the used regularisation scheme. Then alternative explanations for the observed accelerated expansion of the universe in the present epoch are introduced which either modify gravity or add a new component of matter, dubbed dark energy. The chapter closes with some comments on attempts to quantise gravity.

Taxonomy of Dark Energy Models

Universe ◽

10.3390/universe7060163 ◽

2021 ◽

Vol 7 (6) ◽

pp. 163

Author(s):

Verónica Motta ◽

Miguel A. García-Aspeitia ◽

Alberto Hernández-Almada ◽

Juan Magaña ◽

Tomás Verdugo

Keyword(s):

Dark Energy ◽

Cold Dark Matter ◽

Accelerated Expansion ◽

Energy Component ◽

The Past ◽

Energy Models ◽

The Status ◽

The Universe ◽

Unknown Component

The accelerated expansion of the Universe is one of the main discoveries of the past decades, indicating the presence of an unknown component: the dark energy. Evidence of its presence is being gathered by a succession of observational experiments with increasing precision in its measurements. However, the most accepted model for explaining the dynamic of our Universe, the so-called Lambda cold dark matter, faces several problems related to the nature of such energy component. This has led to a growing exploration of alternative models attempting to solve those drawbacks. In this review, we briefly summarize the characteristics of a (non-exhaustive) list of dark energy models as well as some of the most used cosmological samples. Next, we discuss how to constrain each model’s parameters using observational data. Finally, we summarize the status of dark energy modeling.

Gamma Astrometric Measurement Experiment: testing General Relativity with a small mission

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308019364 ◽

2007 ◽

Vol 3 (S248) ◽

pp. 290-291 ◽

Cited By ~ 1

Author(s):

A. Vecchiato ◽

M. G. Lattanzi ◽

M. Gai ◽

R. Morbidelli

Keyword(s):

General Relativity ◽

Solar Eclipse ◽

Galactic Center ◽

The Sun ◽

Measurement Experiment ◽

The One ◽

First Time ◽

Bending Of Light

AbstractGAME (Gamma Astrometric Measurement Experiment) is a concept for an experiment whose goal is to measure from space the γ parameter of the Parameterized Post-Newtonian formalism, by means of a satellite orbiting at 1 AU from the Sun and looking as close as possible to its limb. This technique resembles the one used during the solar eclipse of 1919, when Dyson, Eddington and collaborators measured for the first time the gravitational bending of light. Simple estimations suggest that, possibly within the budget of a small mission, one could reach the 10−6level of accuracy with ~106observations of relatively bright stars at about 2° apart from the Sun. Further simulations show that this result could be reached with only 20 days of measurements on stars ofV≤ 17 uniformly distributed. A quick look at real star densities suggests that this result could be greatly improved by observing particularly crowded regions near the galactic center.

INFLATION, QUINTESSENCE PROBLEM AND VARYING SPEED OF LIGHT

Modern Physics Letters A ◽

10.1142/s0217732302006370 ◽

2002 ◽

Vol 17 (05) ◽

pp. 295-302

Author(s):

SUBENOY CHAKRABORTY

Keyword(s):

Cosmological Constant ◽

Accelerated Expansion ◽

Speed Of Light ◽

In this paper it is shown that the present accelerated expansion of the Universe can be explained only by considering variation of the speed of light, without taking into account the cosmological constant or quintessence matter.