Research

13 pages, 651 KiB

Open AccessArticle

Nonsingular Phantom Cosmology in Five-Dimensional f(R, T) Gravity

by Rakesh Ranjan Sahoo, Kamal Lochan Mahanta and Saibal Ray

Universe 2022, 8(11), 573; https://doi.org/10.3390/universe8110573 - 30 Oct 2022

Cited by 3 | Viewed by 1331

We obtain exact solutions to the field equations for five-dimensional locally rotationally symmetric (LRS) Bianchi type-I spacetime in the

f (R, T)

theory of gravity, where specifically, the following three cases are considered: (i) [...] Read more.

We obtain exact solutions to the field equations for five-dimensional locally rotationally symmetric (LRS) Bianchi type-I spacetime in the

f (R, T)

theory of gravity, where specifically, the following three cases are considered: (i)

f (R, T) = μ (R + T)

, (ii)

f (R, T) = R μ + R T μ^{2}

, and (iii)

f (R, T) = R + μ R^{2} + μ T

, where R and T, respectively, are the Ricci scalar and trace of the energy–momentum tensor. It is found that the equation of state (EOS) parameter w is governed by the parameter

μ

involved in the

f (R, T)

expressions. We fine-tune the parameter

μ

to obtain the effect of phantom energy in the model. However, we also restrict this parameter to obtain a stable model of the universe. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

19 pages, 626 KiB

Open AccessArticle

Classification of Circular Equatorial Orbits around Regular Rotating Black Holes and Solitons with the de Sitter/ Phantom Interiors

by Irina Dymnikova, Anna Dobosz and Bożena Sołtysek

Universe 2022, 8(2), 65; https://doi.org/10.3390/universe8020065 - 20 Jan 2022

Cited by 4 | Viewed by 2041

Abstract

We study the basic properties of the circular equatorial orbits for the regular axially symmetric solutions, obtained with using the Gürses–Gürsey formalism which includes the Newman–Janis algorithm, from regular spherically symmetric metrics of the Kerr–Schild class specified by [...] Read more.

We study the basic properties of the circular equatorial orbits for the regular axially symmetric solutions, obtained with using the Gürses–Gürsey formalism which includes the Newman–Janis algorithm, from regular spherically symmetric metrics of the Kerr–Schild class specified by

T_{t}^{t} = T_{r}^{r}

. Solutions of this class describe regular rotating black holes and spinning solitons replacing naked singularities. All these objects have the interior de Sitter equatorial disk, and can have two kinds of interiors determined by the energy conditions. One of them contains an additional interior de Sitter vacuum

S

-surface with the de Sitter disk as a bridge, whose internal cavities are filled with a phantom fluid. We study in detail the innermost equatorial circular orbits and show that in the field of spinning solitons, the innermost orbits exist within ergoregions related to phantom regions. We show also that around spinning solitons there can exist four corotating light rings and around a regular black hole, one corotating light ring, which is stable for a certain class of black holes. For all objects there exists one counterrotating light ring. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

25 pages, 891 KiB

Open AccessArticle

Asymptotic Solutions of a Generalized Starobinski Model: Kinetic Dominance, Slow Roll and Separatrices

by Elena Medina and Luis Martínez Alonso

Universe 2021, 7(12), 500; https://doi.org/10.3390/universe7120500 - 15 Dec 2021

Viewed by 1922

Abstract

We consider a generalized Starobinski inflationary model. We present a method for computing solutions as generalized asymptotic expansions, both in the kinetic dominance stage (psi series solutions) and in the slow roll stage (asymptotic expansions of the separatrix solutions). These asymptotic expansions are [...] Read more.

We consider a generalized Starobinski inflationary model. We present a method for computing solutions as generalized asymptotic expansions, both in the kinetic dominance stage (psi series solutions) and in the slow roll stage (asymptotic expansions of the separatrix solutions). These asymptotic expansions are derived in the framework of the Hamilton-Jacobi formalism where the Hubble parameter is written as a function of the inflaton field. They are applied to determine the values of the inflaton field when the inflation period starts and ends as well as to estimate the corresponding amount of inflation. As a consequence, they can be used to select the appropriate initial conditions for determining a solution with a previously fixed amount of inflation. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

13 pages, 14962 KiB

Open AccessEditor’s ChoiceArticle

Effect of the Cubic Torus Topology on Cosmological Perturbations

by Maxim Eingorn, Ezgi Canay, Jacob M. Metcalf, Maksym Brilenkov and Alexander Zhuk

Universe 2021, 7(12), 469; https://doi.org/10.3390/universe7120469 - 30 Nov 2021

Cited by 5 | Viewed by 2145

Abstract

We study the effect of the cubic torus topology of the Universe on scalar cosmological perturbations which define the gravitational potential. We obtain three alternative forms of the solution for both the gravitational potential produced by point-like masses, and the corresponding force. The [...] Read more.

We study the effect of the cubic torus topology of the Universe on scalar cosmological perturbations which define the gravitational potential. We obtain three alternative forms of the solution for both the gravitational potential produced by point-like masses, and the corresponding force. The first solution includes the expansion of delta-functions into Fourier series, exploiting periodic boundary conditions. The second one is composed of summed solutions of the Helmholtz equation for the original mass and its images. Each of these summed solutions is the Yukawa potential. In the third formula, we express the Yukawa potentials via Ewald sums. We show that for the present Universe, both the bare summation of Yukawa potentials and the Yukawa-Ewald sums require smaller numbers of terms to yield the numerical values of the potential and the force up to desired accuracy. Nevertheless, the Yukawa formula is yet preferable owing to its much simpler structure. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

9 pages, 256 KiB

Open AccessArticle

Wave Functional of the Universe and Time

by Natalia Gorobey, Alexander Lukyanenko and Alexander V. Goltsev

Universe 2021, 7(11), 452; https://doi.org/10.3390/universe7110452 - 19 Nov 2021

Cited by 4 | Viewed by 1309

Abstract

A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. To determine the physical wave functional, the quantum principle of least action is formulated as a secular equation for the corresponding action [...] Read more.

A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. To determine the physical wave functional, the quantum principle of least action is formulated as a secular equation for the corresponding action operator. Its solution, the wave functional, is an invariant of general covariant transformations of spacetime. In the new formulation, the history of the evolution of the universe is described in terms of coordinate time together with arbitrary lapse and shift functions, which makes this description close to the formulation of the principle of general covariance in the classical theory of Einstein’s gravity. In the new formulation of quantum theory, an invariant parameter of the evolutionary time of the universe is defined, which is a generalization of the classical geodesic time measured by a standard clock along time-like geodesics. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

35 pages, 485 KiB

Open AccessArticle

Coherent States for Fractional Powers of the Harmonic Oscillator Hamiltonian

by Kristina Giesel and Almut Vetter

Universe 2021, 7(11), 442; https://doi.org/10.3390/universe7110442 - 16 Nov 2021

Cited by 2 | Viewed by 1611

Abstract

Inspired by special and general relativistic systems that can have Hamiltonians involving square roots or more general fractional powers, in this article, we address the question of how a suitable set of coherent states for such systems can be obtained. This becomes a [...] Read more.

Inspired by special and general relativistic systems that can have Hamiltonians involving square roots or more general fractional powers, in this article, we address the question of how a suitable set of coherent states for such systems can be obtained. This becomes a relevant topic if the semiclassical sector of a given quantum theory is to be analysed. As a simple setup, we consider the toy model of a deparametrised system with one constraint that involves a fractional power of the harmonic oscillator Hamiltonian operator, and we discuss two approaches to finding suitable coherent states for this system. In the first approach, we consider Dirac quantisation and group averaging, as have been used by Ashtekar et al., but only for integer powers of operators. Our generalisation to fractional powers yields in the case of the toy model a suitable set of coherent states. The second approach is inspired by coherent states based on a fractional Poisson distribution introduced by Laskin, which however turn out not to satisfy all properties to yield good semiclassical results for the operators considered here and in particular do not satisfy a resolution of identity as claimed. Therefore, we present a generalisation of the standard harmonic oscillator coherent states to states involving fractional labels, which approximate the fractional operators in our toy model semiclassically more accurately and satisfy a resolution of identity. In addition, motivated by the way the proof of the resolution of identity is performed, we consider these kind of coherent states also for the polymerised harmonic oscillator and discuss their semiclassical properties. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

22 pages, 3234 KiB

Open AccessArticle

Analog Particle Production Model for General Classes of Taub-NUT Black Holes

by Joshua Foo, Michael R. R. Good and Robert B. Mann

Universe 2021, 7(9), 350; https://doi.org/10.3390/universe7090350 - 20 Sep 2021

Cited by 6 | Viewed by 1696

Abstract

We derive a correspondence between the Hawking radiation spectra emitted from general classes of Taub-NUT black holes with that induced by the relativistic motion of an accelerated Dirichlet boundary condition (i.e., a perfectly reflecting mirror) in (1+1)-dimensional flat spacetime. We demonstrate that the [...] Read more.

We derive a correspondence between the Hawking radiation spectra emitted from general classes of Taub-NUT black holes with that induced by the relativistic motion of an accelerated Dirichlet boundary condition (i.e., a perfectly reflecting mirror) in (1+1)-dimensional flat spacetime. We demonstrate that the particle and energy spectra is thermal at late times and that particle production is suppressed by the NUT parameter. We also compute the radiation spectrum in the rotating, electrically charged (Kerr–Newman) Taub-NUT scenario, and the extremal case, showing, explicitly, how these parameters affect the outgoing particle and energy fluxes. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

17 pages, 406 KiB

Open AccessArticle

Schwarzschild-like Wormholes in Asymptotically Safe Gravity

by Geová Alencar and Matheus Nilton

Universe 2021, 7(9), 332; https://doi.org/10.3390/universe7090332 - 08 Sep 2021

Cited by 6 | Viewed by 2265

Abstract

In this paper, we analyze the Schwarzschild-like wormhole in the Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented via renormalization group methods, which, as consequence, provides a new tensor

X_{μ ν}

as a source to improved field equations, and promotes the [...] Read more.

In this paper, we analyze the Schwarzschild-like wormhole in the Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented via renormalization group methods, which, as consequence, provides a new tensor

X_{μ ν}

as a source to improved field equations, and promotes the Newton’s constant into a running coupling constant. In particular, we check whether the radial energy conditions are satisfied and compare with the results obtained from the usual theory. We show that only in the particular case of the wormhole being asymptotically flat(Schwarzschild Wormholes) that the radial energy conditions are satisfied at the throat, depending on the chosen values for its radius

r_{0}

. In contrast, in the general Schwarzschild-like case, there is no possibility of the energy conditions being satisfied nearby the throat, as in the usual case. After that, we calculate the radial state parameter,

ω (r)

, in

r_{0}

, in order to verify what type of cosmologic matter is allowed at the wormhole throat, and we show that in both cases there is the possibility of the presence of exotic matter, phantom or quintessence-like matter. Finally, we give the

ω (r)

solutions for all regions of space. Interestingly, we find that Schwarzschild-like Wormholes with excess of solid angle of the sphere in the asymptotic limit have the possibility of having non-exotic matter as source for certain values of the radial coordinate r. Furthermore, it was observed that quantum gravity corrections due the ASG necessarily imply regions with phantom-like matter, both for Schwarzschild and for Schwarzschild-like wormholes. This reinforces the supposition that a phantom fluid is always present for wormholes in this context. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

26 pages, 766 KiB

Open AccessArticle

Counting Tensor Rank Decompositions

by Dennis Obster and Naoki Sasakura

Universe 2021, 7(8), 302; https://doi.org/10.3390/universe7080302 - 15 Aug 2021

Cited by 5 | Viewed by 2016

Abstract

Tensor rank decomposition is a useful tool for geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able to estimate how many tensor rank [...] Read more.

Tensor rank decomposition is a useful tool for geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able to estimate how many tensor rank decompositions can approximate a given tensor. More precisely, finding an approximate symmetric tensor rank decomposition of a symmetric tensor Q with an error allowance

Δ

is to find vectors

ϕ^{i}

satisfying

∥ Q - \sum_{i = 1}^{R} ϕ^{i} \otimes ϕ^{i} \dots \otimes ϕ^{i} ∥^{2} \leq Δ

. The volume of all such possible

ϕ^{i}

is an interesting quantity which measures the amount of possible decompositions for a tensor Q within an allowance. While it would be difficult to evaluate this quantity for each Q, we find an explicit formula for a similar quantity by integrating over all Q of unit norm. The expression as a function of

Δ

is given by the product of a hypergeometric function and a power function. By combining new numerical analysis and previous results, we conjecture a formula for the critical rank, yielding an estimate for the spacetime degrees of freedom of the CTM. We also extend the formula to generic decompositions of non-symmetric tensors in order to make our results more broadly applicable. Interestingly, the derivation depends on the existence (convergence) of the partition function of a matrix model which previously appeared in the context of the CTM. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

29 pages, 2240 KiB

Open AccessArticle

Tractor Beams, Pressor Beams and Stressor Beams in General Relativity

by Jessica Santiago, Sebastian Schuster and Matt Visser

Universe 2021, 7(8), 271; https://doi.org/10.3390/universe7080271 - 27 Jul 2021

Cited by 8 | Viewed by 2603

Abstract

The metrics of general relativity generally fall into two categories: those which are solutions of the Einstein equations for a given source energy-momentum tensor and the “reverse engineered” metrics—metrics bespoke for a certain purpose. Their energy-momentum tensors are then calculated by inserting these [...] Read more.

The metrics of general relativity generally fall into two categories: those which are solutions of the Einstein equations for a given source energy-momentum tensor and the “reverse engineered” metrics—metrics bespoke for a certain purpose. Their energy-momentum tensors are then calculated by inserting these into the Einstein equations. This latter approach has found frequent use when confronted with creative input from fiction, wormholes and warp drives being the most famous examples. In this paper, we again take inspiration from fiction and see what general relativity can tell us about the possibility of a gravitationally induced tractor beam. We base our construction on warp drives and show how versatile this ansatz alone proves to be. Not only can we easily find tractor beams (attracting objects), but repulsor/pressor beams are just as attainable, and a generalization to “stressor” beams is seen to present itself quite naturally. We show that all of these metrics would violate various energy conditions. This provides an opportunity to ruminate on the meaning of energy conditions as such and what we can learn about whether an arbitrarily advanced civilization might have access to such beams. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

17 pages, 705 KiB

Open AccessArticle

Braneworld Inspires Cosmological Implications of Barrow Holographic Dark Energy

by Shamaila Rani and Nadeem Azhar

Universe 2021, 7(8), 268; https://doi.org/10.3390/universe7080268 - 27 Jul 2021

Cited by 16 | Viewed by 2134

Abstract

In the present manuscript, the evolution of the cosmic parameters and planes are being investigated in the framework of the DGP braneworld model. In this scenario, the interaction

Γ

between the Barrow holographic dark energy model (whose infrared cutoff scale is set by [...] Read more.

In the present manuscript, the evolution of the cosmic parameters and planes are being investigated in the framework of the DGP braneworld model. In this scenario, the interaction

Γ

between the Barrow holographic dark energy model (whose infrared cutoff scale is set by Hubble and event horizons) and pressureless dark matter are considered. We check the behavior of different cosmological parameters such as Hubble, equation of state, deceleration and squared speed of sound from the early matter-dominated era until the late-time acceleration. It is found that the range of Hubble parameter lies in the interval

95_{- 35}^{+ 35}

(for Hubble horizon) and

97_{- 23}^{+ 23}

(for event horizon). For both horizons, the equation of state parameter favors the phantom dominant era as well as the

Λ

CDM model while the deceleration parameter illustrates the accelerated expansion of the universe. Furthermore, stability of the underlying model is found through squared speed of sound. Furthermore, it is observed that

ω - ω_{ϑ}^{'}

plane corresponds to freezing and thawing region for Hubble and event horizons, respectively. Furthermore, statefinder plane shows the

Λ

CDM and Chaplygin gas behavior for both models. Finally, we investigate the thermodynamical nature of the underlying model through Barrow entropy as horizon entropy and found validity for both horizons. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

10 pages, 285 KiB

Open AccessCommunication

Deviation from Slow-Roll Regime in the EGB Inflationary Models with r ∼

N_{e}^{- 1}

by Ekaterina O. Pozdeeva

Universe 2021, 7(6), 181; https://doi.org/10.3390/universe7060181 - 04 Jun 2021

Cited by 4 | Viewed by 1710

Abstract

We consider Einstein–Gauss–Bonnet (EGB) inflationary models using the effective potential approach. We present evolution equations in the slow-roll regime using the effective potential and the tensor-to-scalar ratio. The choice of the effective potential is related to an expression of the spectral index in [...] Read more.

We consider Einstein–Gauss–Bonnet (EGB) inflationary models using the effective potential approach. We present evolution equations in the slow-roll regime using the effective potential and the tensor-to-scalar ratio. The choice of the effective potential is related to an expression of the spectral index in terms of e-folding number

N_{e}

. The satisfaction of the slow-roll regime is mostly related to the form of the tensor-to-scalar ratio r. The case of

r \sim 1 / N_{e}^{2}

leads to a generalization of

α

-attractors inflationary parameters to Einstein–Gauss–Bonnet gravity with exponential effective potential. Moreover, the cosmological attractors include models with

r \sim 1 / N_{e}

. And we check the satisfaction of the slow-roll regime during inflation for models with

r \sim 1 / N_{e}

. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

25 pages, 365 KiB

Open AccessArticle

Quantum State Evolution in an Environment of Cosmological Perturbations

by Zbigniew Haba

Universe 2021, 7(5), 117; https://doi.org/10.3390/universe7050117 - 21 Apr 2021

Cited by 3 | Viewed by 1615

Abstract

We study the pure and thermal states of quantized scalar and tensor perturbations in various epochs of Universe evolution. We calculate the density matrix of non-relativistic particles in an environment of these perturbations. We show that particle’s motion can be described by a [...] Read more.

We study the pure and thermal states of quantized scalar and tensor perturbations in various epochs of Universe evolution. We calculate the density matrix of non-relativistic particles in an environment of these perturbations. We show that particle’s motion can be described by a stochastic equation with a noise coming from the cosmological environment. We investigate the squeezing of Gaussian wave packets in different epochs and its impact on the noise of quantized cosmological perturbations. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

15 pages, 403 KiB

Open AccessArticle

Cosmic Evolution of Viscous QCD Epoch in Causal Eckart Frame

by Eman Abdel Hakk, Abdel Nasser Tawfik, Afaf Nada and Hayam Yassin

Universe 2021, 7(5), 112; https://doi.org/10.3390/universe7050112 - 21 Apr 2021

Cited by 3 | Viewed by 1952

Abstract

It is conjectured that in cosmological applications the particle current is not modified but finite heat or energy flow. Therefore, comoving Eckart frame is a suitable choice, as it merely ceases the charge and particle diffusion and conserves charges and particles. The cosmic [...] Read more.

It is conjectured that in cosmological applications the particle current is not modified but finite heat or energy flow. Therefore, comoving Eckart frame is a suitable choice, as it merely ceases the charge and particle diffusion and conserves charges and particles. The cosmic evolution of viscous hadron and parton epochs in casual and non-casual Eckart frame is analyzed. By proposing equations of state deduced from recent lattice QCD simulations including pressure p, energy density

ρ

, and temperature T, the Friedmann equations are solved. We introduce expressions for the temporal evolution of the Hubble parameter

\dot{H}

, the cosmic energy density

\dot{ρ}

, and the share

\dot{η}

and the bulk viscous coefficient

\dot{ζ}

. We also suggest how the bulk viscous pressure

Π

could be related to H. We conclude that the relativistic theory of fluids, the Eckart frame, and the finite viscous coefficients play essential roles in the cosmic evolution, especially in the hadron and parton epochs. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

► Show Figures

Figure 1

7 pages, 253 KiB

Open AccessCommunication

The Effect of Higher Dimensional QCD Operators on the Spectroscopy of Bottom-Up Holographic Models

by Sergey Afonin

Universe 2021, 7(4), 102; https://doi.org/10.3390/universe7040102 - 15 Apr 2021

Cited by 3 | Viewed by 1585

Abstract

Within the bottom-up holographic approach to QCD, the highly excited hadrons are identified with the bulk normal modes in the fifth “holographic” dimension. We show that additional states in the same mass range can appear also from taking into consideration the 5D fields [...] Read more.

Within the bottom-up holographic approach to QCD, the highly excited hadrons are identified with the bulk normal modes in the fifth “holographic” dimension. We show that additional states in the same mass range can appear also from taking into consideration the 5D fields dual to higher dimensional QCD operators. The possible effects of these operators have not been taken into account in virtually any phenomenological applications. Using the scalar case as the simplest example, we demonstrate that the additional higher dimensional operators lead to a large degeneracy of highly excited states in the soft wall holographic model, and in the hard wall holographic model, they result in a proliferation of excited states. The considered model can be viewed as the first analytical toy model predicting a one-to-one mapping of the excited meson states to definite QCD operators, to which they prefer to couple. Full article

(This article belongs to the Special Issue Cosmological Models, Quantum Theories and Astrophysical Observations)

Journal Menu

Journal Browser

Cosmological Models, Quantum Theories and Astrophysical Observations

Share This Special Issue

Special Issue Editors

Special Issue Information

Published Papers (15 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI