2024

Jump to: 2023, 2022

21 pages, 378 KiB

Open AccessArticle

Reconstructing Modified and Alternative Theories of Gravity

by Dalia Saha, Manas Chakrabortty and Abhik Kumar Sanyal

Universe 2024, 10(1), 44; https://doi.org/10.3390/universe10010044 - 17 Jan 2024

Viewed by 971

A viable radiation-dominated era in the early universe is best described by the standard (FLRW) model of cosmology. In this short review, we demonstrate reconstruction of the forms of

F (R)

in the modified theory of gravity and the metric compatible [...] Read more.

A viable radiation-dominated era in the early universe is best described by the standard (FLRW) model of cosmology. In this short review, we demonstrate reconstruction of the forms of

F (R)

in the modified theory of gravity and the metric compatible

F (T)

together with the symmetric

F (Q)

in alternative teleparallel theories of gravity, from different perspectives, primarily rendering emphasis on a viable FLRW radiation era. Inflation has also been studied for a particular choice of the scalar potential. The inflationary parameters are found to agree appreciably with the recently released observational data. Full article

2023

Jump to: 2024, 2022

14 pages, 323 KiB

Open AccessArticle

Fab-Four Cosmography to Tackle the Hubble Tension

by Celia Escamilla-Rivera, José María de Albornoz-Caratozzolo and Sebastián Nájera

Universe 2023, 9(7), 311; https://doi.org/10.3390/universe9070311 - 28 Jun 2023

Cited by 2 | Viewed by 850

Abstract

In the context of the Fab-Four theory of gravity in a Friedmann-Lemaître-Robertson-Walker background, in this work we use the cosmography approach to study a particular self-tuning filter solution focused on a zero-curvature fixed point to study the

H_{0}

tension. In this scheme, [...] Read more.

In the context of the Fab-Four theory of gravity in a Friedmann-Lemaître-Robertson-Walker background, in this work we use the cosmography approach to study a particular self-tuning filter solution focused on a zero-curvature fixed point to study the

H_{0}

tension. In this scheme, the equations restrict the universe’s evolution to certain scenarios, including radiation-like expansion, matter-like expansion, and late-time acceleration. Furthermore, we build the cosmographic series of the Fab-Four theory to obtain the kinematic parameters as the Hubble constant

H_{0}

and the deceleration parameter

q_{0}

for all the scenarios mentioned. Finally, we compare our results to find that it is possible to alleviate the current discrepancy on

H_{0}

by considering specific requirements on the free parameters of the Fab-Four theory through a self-tuning filter. Full article

10 pages, 832 KiB

Open AccessCommunication

Production of Primordial Black Holes in Improved E-Models of Inflation

by Daniel Frolovsky and Sergei V. Ketov

Universe 2023, 9(6), 294; https://doi.org/10.3390/universe9060294 - 16 Jun 2023

Cited by 3 | Viewed by 843

Abstract

E-type

α

-attractor models of single-field inflation were generalized further in order to accommodate production of primordial black holes (PBHs) via adding a near-inflection point to the inflaton scalar potential at smaller scales, in good agreement with measurements of cosmic microwave background (CMB) [...] Read more.

E-type

α

-attractor models of single-field inflation were generalized further in order to accommodate production of primordial black holes (PBHs) via adding a near-inflection point to the inflaton scalar potential at smaller scales, in good agreement with measurements of cosmic microwave background (CMB) radiation. A minimal number of new parameters were used but their fine-tuning was maximized in order to increase the possible masses of PBHs formed during an ultra-slow-roll phase, leading to a large enhancement in the power spectrum of scalar (curvature) perturbations by 6 or 7 orders of magnitude against the power spectrum of perturbations observed in CMB. It was found that extreme fine-tuning of the parameters in our models can lead to the formation of moon-sized PBHs, with masses of up to

10^{26}

g, still in agreement with CMB observations. Quantum corrections are known to lead to the perturbative upper bound on the amplitude of large scalar perturbations responsible for PBH production. The quantum (one-loop) corrections in our models were found to be suppressed by one order of magnitude for PBHs with masses of approximately

10^{19}

g, which may form the whole dark matter in the Universe. Full article

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15 pages, 471 KiB

Open AccessArticle

Newtonian Fractional-Dimension Gravity and Galaxies without Dark Matter

by Gabriele U. Varieschi

Universe 2023, 9(6), 246; https://doi.org/10.3390/universe9060246 - 24 May 2023

Cited by 4 | Viewed by 941

Abstract

We apply Newtonian fractional-dimension gravity (NFDG), an alternative gravitational model, to some notable cases of galaxies with little or no dark matter. In the case of the ultra-diffuse galaxy AGC 114905, we show that NFDG methods can effectively reproduce the observed rotation curve [...] Read more.

We apply Newtonian fractional-dimension gravity (NFDG), an alternative gravitational model, to some notable cases of galaxies with little or no dark matter. In the case of the ultra-diffuse galaxy AGC 114905, we show that NFDG methods can effectively reproduce the observed rotation curve using a variable fractional dimension

D (R)

, as was performed for other galaxies in previous studies. For AGC 114905, we obtain a variable dimension in the range

D \approx

2.2–3.2, but our fixed D = 3 curve can still fit all the experimental data within their error bars. This confirms other studies indicating that the dynamics of this galaxy can be described almost entirely by the baryonic mass distribution alone. In the case of NGC 1052-DF2, we use an argument based on the NFDG extension of the virial theorem applied to the velocity dispersion of globular clusters showing that, in general, discrepancies between observed and predicted velocity dispersions can be attributed to an overall fractal dimension

D < 3

of the astrophysical structure considered, and not to the presence of dark matter. For NGC 1052-DF2, we estimate

D \approx 2.9

, thus confirming that this galaxy almost follows standard Newtonian behavior. We also consider the case of the Bullet Cluster merger (1E0657-56), assumed to be one of the strongest proofs of dark matter existence. A simplified but effective NFDG model of the collision shows that the observed infall velocity of this merger can be explained by a fractional dimension of the system in the range

D ≃

2.4–2.5, again, without using any dark matter. Full article

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25 pages, 654 KiB

Open AccessArticle

The Finsler Spacetime Condition for (α,β)-Metrics and Their Isometries

by Nicoleta Voicu, Annamária Friedl-Szász, Elena Popovici-Popescu and Christian Pfeifer

Universe 2023, 9(4), 198; https://doi.org/10.3390/universe9040198 - 20 Apr 2023

Cited by 1 | Viewed by 1177

Abstract

For the general class of pseudo-Finsler spaces with

(α, β)

-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has a Lorentzian signature on a conic subbundle of [...] Read more.

For the general class of pseudo-Finsler spaces with

(α, β)

-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has a Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future-pointing time-like vectors is ensured. The identified

(α, β)

-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an

(α, β)

-metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all

(α, β)

-metrics which admit isometries that are not isometries of a. Full article

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15 pages, 945 KiB

Open AccessReview

Resolution of Cosmological Singularity in Hořava–Lifshitz Cosmology

by Ewa Czuchry

Universe 2023, 9(4), 160; https://doi.org/10.3390/universe9040160 - 25 Mar 2023

Cited by 1 | Viewed by 945

Abstract

The standard ΛCDM model, despite its agreement with observational data, still has some issues unaddressed, such as the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However, there appeared the Hořava–Lifshitz (HL) theory of gravity, in which equations [...] Read more.

The standard ΛCDM model, despite its agreement with observational data, still has some issues unaddressed, such as the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However, there appeared the Hořava–Lifshitz (HL) theory of gravity, in which equations governing cosmological evolution include a new term scaling similarly as the dark radiation term in the Friedmann equations, enabling a bounce of the universe instead of initial singularity. This review describes past works on the stability of such a bounce in different formulations of HL theory, an initial detailed balance scenario, and further projectable versions containing higher than quadratic terms to the original action. Full article

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18 pages, 361 KiB

Open AccessReview

Geometric Outlines of the Gravitational Lensing and Its Astronomic Applications

by Bin Shen and Mingyang Yu

Universe 2023, 9(3), 153; https://doi.org/10.3390/universe9030153 - 17 Mar 2023

Viewed by 1277

Abstract

Gravitational lensing is a topic of great application value in the field of astronomy. The properties and research methods of gravitational lensing are closely related to the geometric and relativistic characteristics of the background universe. This review focuses on the theoretical research and [...] Read more.

Gravitational lensing is a topic of great application value in the field of astronomy. The properties and research methods of gravitational lensing are closely related to the geometric and relativistic characteristics of the background universe. This review focuses on the theoretical research and application of strong lenses and weak lenses. We first introduce the basic principles of gravitational lensing, focusing on the geometric basis of geometric lensing, the representation of deflection angles, and the curvature relationship in different geometric spaces. In addition, we summarize the wide range of applications of gravitational lensing, including the application of strong gravitational lensing in Schwarzschild black holes, time delay, the cosmic shearing based on weak lensing, the applications in signal extraction, dark matter, and dark energy. In astronomy, through the use of advanced astronomical instruments and computers, analyzing gravitational lensing effects to understand the structure of galaxies in the universe is an important topic at present. It is foreseeable that gravitational lensing will continue to play an important role in the study of cosmology and will enrich our understanding of the universe. Full article

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21 pages, 373 KiB

Open AccessArticle

On Born’s Reciprocal Relativity, Algebraic Extensions of the Yang and Quaplectic Algebra, and Noncommutative Curved Phase Spaces

by Carlos Castro Perelman

Universe 2023, 9(3), 144; https://doi.org/10.3390/universe9030144 - 09 Mar 2023

Cited by 1 | Viewed by 800

Abstract

After a brief introduction of Born’s reciprocal relativity theory is presented, we review the construction of the

d e f o r m e d

quaplectic group that is given by the semi-direct product of

U (1, 3)

with the [...] Read more.

After a brief introduction of Born’s reciprocal relativity theory is presented, we review the construction of the

d e f o r m e d

quaplectic group that is given by the semi-direct product of

U (1, 3)

with the

d e f o r m e d

(noncommutative) Weyl–Heisenberg group corresponding to

n o n c o m m u t a t i v e

fiber coordinates and momenta

[X_{a}, X_{b}] \neq 0

;

[P_{a}, P_{b}] \neq 0

. This construction leads to more general algebras given by a two-parameter family of deformations of the quaplectic algebra, and to further algebraic extensions involving antisymmetric tensor coordinates and momenta of higher ranks

[X_{a_{1} a_{2} \dots a_{n}}, X_{b_{1} b_{2} \dots b_{n}}] \neq 0

;

[P_{a_{1} a_{2} \dots a_{n}}, P_{b_{1} b_{2} \dots b_{n}}] \neq 0

. We continue by examining algebraic extensions of the Yang algebra in extended noncommutative phase spaces and compare them with the above extensions of the deformed quaplectic algebra. A solution is found for the exact analytical mapping of the noncommuting

x^{μ}, p^{μ}

operator variables (associated to an 8D curved phase space) to the canonical

Y^{A}, Π^{A}

operator variables of a flat 12D phase space. We explore the geometrical implications of this mapping which provides, in the

c l a s s i c a l

limit, the embedding functions

Y^{A} (x, p), Π^{A} (x, p)

of an 8D curved phase space into a flat 12D phase space background. The latter embedding functions determine the functional forms of the base spacetime metric

g_{μ ν} (x, p)

, the fiber metric of the vertical space

h^{a b} (x, p)

, and the nonlinear connection

N_{a μ} (x, p)

associated with the 8D cotangent space of the 4D spacetime. Consequently, we find a direct link between noncommutative curved phase spaces in lower dimensions and commutative flat phase spaces in higher dimensions. Full article

27 pages, 1086 KiB

Open AccessArticle

Realization of Bounce in a Modified Gravity Framework and Information Theoretic Approach to the Bouncing Point

by Sanghati Saha and Surajit Chattopadhyay

Universe 2023, 9(3), 136; https://doi.org/10.3390/universe9030136 - 06 Mar 2023

Cited by 5 | Viewed by 1341

Abstract

In this work, we report a study on bouncing cosmology with modified generalized Chaplygin Gas (mgCG) in a bulk viscosity framework. Reconstruction schemes were demonstrated in Einstein and modified

f (T)

gravity framework under the purview of viscous cosmological settings. We [...] Read more.

In this work, we report a study on bouncing cosmology with modified generalized Chaplygin Gas (mgCG) in a bulk viscosity framework. Reconstruction schemes were demonstrated in Einstein and modified

f (T)

gravity framework under the purview of viscous cosmological settings. We also took non-viscous cases into account. We studied the equation of state (EoS) parameter under various circumstances and judged the stability of the models through the sign of the squared speed of sound. We observed the mgCG behaving like avoidance of Big Rip in the presence of bulk viscosity at the turnaround point and in non-viscous cases, a phantom-like behavior appears. The turnaround point equation of state parameter crosses the phantom boundary, violating NEC. The role of the mgCG’s model parameters was also investigated before and after the bounce. A Hubble flow dynamics was carried out and, it was revealed that mgCG is capable of realizing an inflationary phase as well as an exit from inflation. An

f (T)

gravitational paradigm was also considered, where the mgCG density was reconstructed in the presence of bulk viscosity. The role of the parameters associated with the bouncing scale factor, describing how fast the bounce takes place, was also studied in this framework. Finally, the reconstructed mgCG turned out to be stable against small perturbations irrespective of the presence of bulk viscosity and modified gravity scenario. Finally, the reconstruction scheme was assessed using statistical analysis, Shannon entropy. Full article

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22 pages, 337 KiB

Open AccessArticle

On the Role of Constraints and Degrees of Freedom in the Hamiltonian Formalism

by Alexey Golovnev

Universe 2023, 9(2), 101; https://doi.org/10.3390/universe9020101 - 16 Feb 2023

Cited by 12 | Viewed by 963

Abstract

Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. It then comes to discussing conjectures of whether all primary constraints correspond to gauge symmetries, and it goes [...] Read more.

Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. It then comes to discussing conjectures of whether all primary constraints correspond to gauge symmetries, and it goes all the way to absolutely wrong claims such as the statement that electrodynamics or gravity only have two physical components each, with others being spurious. One has to be very careful because non-dynamical, or constrained, does not mean unphysical. In this article, I give a pedagogical introduction to the degenerate Hamiltonian systems, showing both very simple mechanical examples and general arguments about how it works. For the familiar field theory models, I explain why the gauge freedom there “hits twice” in the sense of producing twice as many first-class constraints as gauge symmetries, and why primary, and only primary, constraints should be put into the total Hamiltonian. Full article

2022

Jump to: 2024, 2023

20 pages, 975 KiB

Open AccessArticle

Bulk Viscous Fluid in Symmetric Teleparallel Cosmology: Theory versus Experiment

by Raja Solanki, Simran Arora, Pradyumn Kumar Sahoo and Pedro H. R. S. Moraes

Universe 2023, 9(1), 12; https://doi.org/10.3390/universe9010012 - 23 Dec 2022

Cited by 6 | Viewed by 1376

Abstract

The standard formulation of General Relativity Theory, in the absence of a cosmological constant, is unable to explain the responsible mechanism for the observed late-time cosmic acceleration. On the other hand, by inserting the cosmological constant in Einstein’s field equations, it is possible [...] Read more.

The standard formulation of General Relativity Theory, in the absence of a cosmological constant, is unable to explain the responsible mechanism for the observed late-time cosmic acceleration. On the other hand, by inserting the cosmological constant in Einstein’s field equations, it is possible to describe the cosmic acceleration, but the cosmological constant suffers from an unprecedented fine-tuning problem. This motivates one to modify Einstein’s spacetime geometry of General Relativity. The

f (Q)

modified theory of gravity is an alternative theory to General Relativity, where the non-metricity scalar Q is the responsible candidate for gravitational interactions. In the present work, we consider a Friedmann–Lemâitre–Robertson–Walker cosmological model dominated by bulk viscous cosmic fluid in

f (Q)

gravity with the functional form

f (Q) = α Q^{n}

, where

α

and n are free parameters of the model. We constrain our model with the Pantheon supernovae dataset of 1048 data points, the Hubble dataset of 31 data points, and the baryon acoustic oscillations dataset consisting of 6 data points. We find that our

f (Q)

cosmological model efficiently describes the observational data. We present the evolution of our deceleration parameter with redshift, and it properly predicts a transition from decelerated to accelerated phases of the universe’s expansion. Furthermore, we present the evolution of density, bulk viscous pressure, and the effective equation of state parameter with redshift. Those show that bulk viscosity in a cosmic fluid is a valid candidate to acquire the negative pressure to drive the cosmic expansion efficiently. We also examine the behavior of different energy conditions to test the viability of our cosmological

f (Q)

model. Furthermore, the statefinder diagnostics are also investigated in order to distinguish among different dark energy models. Full article

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13 pages, 400 KiB

Open AccessArticle

Cooling Process of White Dwarf Stars in Palatini f(R) Gravity

by Surajit Kalita, Lupamudra Sarmah and Aneta Wojnar

Universe 2022, 8(12), 647; https://doi.org/10.3390/universe8120647 - 05 Dec 2022

Cited by 6 | Viewed by 1144

Abstract

A simple cooling model of white dwarf stars is re-analyzed in Palatini

f (R)

gravity. Modified gravity affects the white dwarf structures and consequently their ages. We find that the resulting super-Chandrasekhar white dwarfs need more time to cool down than [...] Read more.

A simple cooling model of white dwarf stars is re-analyzed in Palatini

f (R)

gravity. Modified gravity affects the white dwarf structures and consequently their ages. We find that the resulting super-Chandrasekhar white dwarfs need more time to cool down than sub-Chandrasekhar ones, or when compared to the Newtonian models. Full article

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13 pages, 343 KiB

Open AccessArticle

Weak Field Limit for Embedding Gravity

by Stanislav Kuptsov, Mikhail Ioffe, Sergey Manida and Sergey Paston

Universe 2022, 8(12), 635; https://doi.org/10.3390/universe8120635 - 29 Nov 2022

Cited by 1 | Viewed by 867

Abstract

We study a perturbation theory for embedding gravity equations in a background for which corrections to the embedding function are linear with respect to corrections to the flat metric. The remaining arbitrariness after solving the linearized field equations is fixed by an assumption [...] Read more.

We study a perturbation theory for embedding gravity equations in a background for which corrections to the embedding function are linear with respect to corrections to the flat metric. The remaining arbitrariness after solving the linearized field equations is fixed by an assumption that the solution is static in the second order. A nonlinear differential equation is obtained, which allows for finding the gravitational potential for a spherically symmetric case if a background embedding is given. An explicit form of a spherically symmetric background parameterized by one function of radius is proposed. It is shown that this function can be chosen in such a way that the gravitational potential is in a good agreement with the observed distribution of dark matter in a galactic halo. Full article

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16 pages, 591 KiB

Open AccessArticle

Galactic Wormhole under Lovelock Gravity

by Koushik Chakraborty, Farook Rahaman, Saibal Ray, Banashree Sen and Debabrata Deb

Universe 2022, 8(11), 581; https://doi.org/10.3390/universe8110581 - 03 Nov 2022

Cited by 7 | Viewed by 1355

Abstract

We explore wormhole geometry in spiral galaxies under the third order Lovelock gravity. Using the cubic spline interpolation technique, we find the rotational velocity of test particles in the halo region of our spiral galaxy from observed values of radial distances and rotational [...] Read more.

We explore wormhole geometry in spiral galaxies under the third order Lovelock gravity. Using the cubic spline interpolation technique, we find the rotational velocity of test particles in the halo region of our spiral galaxy from observed values of radial distances and rotational velocities. Taking this value of the rotational velocity, we are able to show that it is possible to present a mathematical model regarding viable existence of wormholes in the galactic halo region of the Milky Way under the Lovelock gravity. A very important result that we obtain from the present investigation is that galactic wormhole in the halo region can exist with normal matter as well as exotic matter. Full article

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20 pages, 1608 KiB

Open AccessArticle

Quintom Fields from Chiral K-Essence Cosmology

by José Socorro, Sinuhé Pérez-Payán, Rafael Hernández-Jiménez, Abraham Espinoza-García and Luis Rey Díaz-Barrón

Universe 2022, 8(10), 548; https://doi.org/10.3390/universe8100548 - 21 Oct 2022

Cited by 9 | Viewed by 1120

Abstract

In this paper, we present an analysis of a chiral cosmological scenario from the perspective of K-essence formalism. In this setup, several scalar fields interact within the kinetic and potential sectors. However, we only consider a flat Friedmann–Robertson–Lamaître–Walker universe coupled minimally to two [...] Read more.

In this paper, we present an analysis of a chiral cosmological scenario from the perspective of K-essence formalism. In this setup, several scalar fields interact within the kinetic and potential sectors. However, we only consider a flat Friedmann–Robertson–Lamaître–Walker universe coupled minimally to two quintom fields: one quintessence and one phantom. We examine a classical cosmological framework, where analytical solutions are obtained. Indeed, we present an explanation of the “big-bang” singularity by means of a “big-bounce”. Moreover, having a barotropic fluid description and for a particular set of parameters, the phantom line is in fact crossed. Additionally, for the quantum counterpart, the Wheeler–DeWitt equation is analytically solved for various instances, where the factor-ordering problem has been taken into account (measured by the factor Q). Hence, this approach allows us to compute the probability density of the previous two classical subcases. It turns out that its behavior is in effect damped as the scale factor and the scalar fields evolve. It also tends towards the phantom sector when the factor ordering constant

Q ≪ 0

. Full article

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10 pages, 294 KiB

Open AccessArticle

Sign Switching Dark Energy from a Running Barrow Entropy

by Sofia Di Gennaro and Yen Chin Ong

Universe 2022, 8(10), 541; https://doi.org/10.3390/universe8100541 - 19 Oct 2022

Cited by 34 | Viewed by 1215

Abstract

Barrow proposed that the area law of the entropy associated with a horizon might receive a “fractal correction” due to quantum gravitational effects—in place of

S \propto A

, we have instead

S \propto A^{1 + δ / 2}

, where [...] Read more.

Barrow proposed that the area law of the entropy associated with a horizon might receive a “fractal correction” due to quantum gravitational effects—in place of

S \propto A

, we have instead

S \propto A^{1 + δ / 2}

, where

0 ⩽ δ ⩽ 1

measures the deviation from the standard area law (

δ = 0

). Based on black hole thermodynamics, we argue that the Barrow entropy should run (i.e., energy scale dependent), which is reasonable given that quantum gravitational corrections are expected to be important only in the high-energy regime. When applied to the Friedmann equation, we demonstrate the possibility that such a running Barrow entropy index could give rise to a dynamical effective dark energy, which is asymptotically positive and vanishing, but negative at the Big Bang. Such a sign switching dark energy could help to alleviate the Hubble tension. Other cosmological implications are discussed. Full article

41 pages, 502 KiB

Open AccessArticle

Metric Gravity in the Hamiltonian Form—Canonical Transformations—Dirac’s Modifications of the Hamilton Method and Integral Invariants of the Metric Gravity

by Alexei M. Frolov

Universe 2022, 8(10), 533; https://doi.org/10.3390/universe8100533 - 14 Oct 2022

Cited by 1 | Viewed by 1059

Abstract

Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the d dimensional Riemann space-time. Theory of canonical transformations, which relates equivalent Hamiltonian formulations of the metric gravity, is investigated in detail. In particular, [...] Read more.

Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the d dimensional Riemann space-time. Theory of canonical transformations, which relates equivalent Hamiltonian formulations of the metric gravity, is investigated in detail. In particular, we have formulated the conditions of canonicity for transformation between the two sets of dynamical variables used in our Hamiltonian formulations of the metric gravity. Such conditions include the ordinary condition of canonicity known in classical Hamilton mechanics, i.e., the exact coincidence of the Poisson (or Laplace) brackets which are determined for both the new and old dynamical Hamiltonian variables. However, in addition to this, any true canonical transformations defined in the metric gravity, which is a constrained dynamical system, must also guarantee the exact conservation of the total Hamiltonians

H_{t}

(in both formulations) and preservation of the algebra of first-class constraints. We show that Dirac’s modifications of the classical Hamilton method contain a number of crucial advantages, which provide an obvious superiority of this method in order to develop various non-contradictory Hamiltonian theories of many physical fields, when a number of gauge conditions are also important. Theory of integral invariants and its applications to the Hamiltonian metric gravity are also discussed. For Hamiltonian dynamical systems with first-class constraints this theory leads to a number of peculiarities some of which have been investigated. Full article

22 pages, 369 KiB

Open AccessReview

Progress in the Composite View of the Newton Gravitational Constant and Its Link to the Planck Scale

by Espen Gaarder Haug

Universe 2022, 8(9), 454; https://doi.org/10.3390/universe8090454 - 30 Aug 2022

Cited by 6 | Viewed by 4714

Abstract

The Newtonian gravity constant G plays a central role in gravitational theory. Researchers have, since at least the 1980s, tried to see if the Newton gravitational constant can be expressed or replaced with more fundamental units, such as the Planck units. However, it [...] Read more.

The Newtonian gravity constant G plays a central role in gravitational theory. Researchers have, since at least the 1980s, tried to see if the Newton gravitational constant can be expressed or replaced with more fundamental units, such as the Planck units. However, it was already pointed out in 1987 that this led to a circular problem; namely, that one must know G to find the Planck units, and that it is therefore of little or no use to express G through the Planck units. This is a view repeated in the literature in recent years, and is held by the physics’ community. However, we will claim that the circular problem was solved a few years ago. In addition, when one expresses the mass from the Compton wavelength formula, this leads to the conclusion that the three universal constants of G, h, and c now can be replaced with only l_p and c to predict observable gravitational phenomena. While there have been several review papers on the Newton gravitational constant, for example, about how to measure it, we have not found a single review paper on the composite view of the gravitational constant. This paper will review the history of, as well as recent progress in, the composite view of the gravitational constant. This should hopefully be a useful supplement in the ongoing research for understanding and discussion of Newton’s gravitational constant. Full article

26 pages, 427 KiB

Open AccessReview

Noncompactified Kaluza–Klein Gravity

by Seyed Meraj Mousavi Rasouli, Shahram Jalalzadeh and Paulo Moniz

Universe 2022, 8(8), 431; https://doi.org/10.3390/universe8080431 - 21 Aug 2022

Cited by 7 | Viewed by 1226

Abstract

We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space–Time–Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans–Dicke theory and the modified Sáez–Ballester theory are briefly explained. [...] Read more.

We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space–Time–Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans–Dicke theory and the modified Sáez–Ballester theory are briefly explained. Finally, we apply the latter to the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological models in arbitrary dimensions and analyze the corresponding solutions. Full article

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