Entropy

Research

Jump to: Review

147 KiB

Open AccessArticle

The Thermal Entropy Density of Spacetime

by Rongjia Yang

Entropy 2013, 15(1), 156-161; https://doi.org/10.3390/e15010156 - 8 Jan 2013

Cited by 9 | Viewed by 7355

Abstract

Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results [...] Read more.

Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

369 KiB

Open AccessArticle

Entropy and Gravity

by Øyvind Grøn

Entropy 2012, 14(12), 2456-2477; https://doi.org/10.3390/e14122456 - 4 Dec 2012

Cited by 15 | Viewed by 9299

Abstract

The effect of gravity upon changes of the entropy of a gravity-dominated system is discussed. In a universe dominated by vacuum energy, gravity is repulsive, and there is accelerated expansion. Furthermore, inhomogeneities are inflated and the universe approaches a state of thermal equilibrium. [...] Read more.

The effect of gravity upon changes of the entropy of a gravity-dominated system is discussed. In a universe dominated by vacuum energy, gravity is repulsive, and there is accelerated expansion. Furthermore, inhomogeneities are inflated and the universe approaches a state of thermal equilibrium. The difference between the evolution of the cosmic entropy in a co-moving volume in an inflationary era with repulsive gravity and a matter-dominated era with attractive gravity is discussed. The significance of conversion of gravitational energy to thermal energy in a process with gravitational clumping, in order that the entropy of the universe shall increase, is made clear. Entropy of black holes and cosmic horizons are considered. The contribution to the gravitational entropy according to the Weyl curvature hypothesis is discussed. The entropy history of the Universe is reviewed. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

► Show Figures

Figure 1

195 KiB

Open AccessArticle

Periodic Cosmological Evolutions of Equation of State for Dark Energy

by Kazuharu Bamba, Ujjal Debnath, Kuralay Yesmakhanova, Petr Tsyba, Gulgasyl Nugmanova and Ratbay Myrzakulov

Entropy 2012, 14(11), 2351-2374; https://doi.org/10.3390/e14112351 - 20 Nov 2012

Cited by 15 | Viewed by 6366

Abstract

We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass ξ(t), σ(t) and ζ (t) functions with two periods being infinite. If the [...] Read more.

We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass ξ(t), σ(t) and ζ (t) functions with two periods being infinite. If the universe can evolve periodically, a non-singular universe can be realized. Furthermore, we examine the cosmological evolution and nature of the equation of state (EoS) of dark energy in the Friedmann–Lemaître–Robertson–Walker cosmology. It is explicitly illustrated that there exist three type models in which the universe always stays in the non-phantom (quintessence) phase, whereas it always evolves in the phantom phase, or the crossing of the phantom divide can be realized. The scalar fields and the corresponding potentials are also analyzed for different types of models. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

► Show Figures

Figure 1

193 KiB

Open AccessArticle

Viscosity in Modified Gravity

by Iver Brevik

Entropy 2012, 14(11), 2302-2310; https://doi.org/10.3390/e14112302 - 12 Nov 2012

Cited by 15 | Viewed by 5211

Abstract

A bulk viscosity is introduced in the formalism of modified gravity. It is shownthat, based on a natural scaling law for the viscosity, a simple solution can be found forquantities such as the Hubble parameter and the energy density. These solutions mayincorporate a [...] Read more.

A bulk viscosity is introduced in the formalism of modified gravity. It is shownthat, based on a natural scaling law for the viscosity, a simple solution can be found forquantities such as the Hubble parameter and the energy density. These solutions mayincorporate a viscosity-induced Big Rip singularity. By introducing a phase transition inthe cosmic fluid, the future singularity can nevertheless in principle be avoided. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

201 KiB

Open AccessArticle

Dark Energy Problem, Physics of Early Universe and Some New Approaches in Gravity

by Alexander Shalyt-Margolin

Entropy 2012, 14(11), 2143-2156; https://doi.org/10.3390/e14112143 - 2 Nov 2012

Cited by 2 | Viewed by 5587

Abstract

The dark energy problem is studied based on the approach associated with the cosmological term in General Relativity that is considered as a dynamic quantity. It is shown that a quantum field theory of the Early Universe (Planck scales) and its limiting transition [...] Read more.

The dark energy problem is studied based on the approach associated with the cosmological term in General Relativity that is considered as a dynamic quantity. It is shown that a quantum field theory of the Early Universe (Planck scales) and its limiting transition at low energy play a significant role. Connection of this problem with Verlinde’s new (entropic) approach to gravity is revealed within the frame of such statement as well as the Generalized Uncertainty Principle (GUP) and Extended Uncertainty Principle (EUP). The implications from the obtained results are presented, and a more rigorous statement of the Concordance Problem in cosmology is treated. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

587 KiB

Open AccessArticle

Accelerating Universe and the Scalar-Tensor Theory

by Yasunori Fujii

Entropy 2012, 14(10), 1997-2035; https://doi.org/10.3390/e14101997 - 19 Oct 2012

Cited by 3 | Viewed by 7291

Abstract

To understand the accelerating universe discovered observationally in 1998, we develop the scalar-tensor theory of gravitation originally due to Jordan, extended only minimally. The unique role of the conformal transformation and frames is discussed particularly from a physical point of view. We show [...] Read more.

To understand the accelerating universe discovered observationally in 1998, we develop the scalar-tensor theory of gravitation originally due to Jordan, extended only minimally. The unique role of the conformal transformation and frames is discussed particularly from a physical point of view. We show the theory to provide us with a simple and natural way of understanding the core of the measurements, Λ_obs ∼ t₀⁻² for the observed values of the cosmological constant and today’s age of the universe both expressed in the Planckian units. According to this scenario of a decaying cosmological constant, Λ_obs is this small only because we are old, not because we fine-tune the parameters. It also follows that the scalar field is simply the pseudo Nambu–Goldstone boson of broken global scale invariance, based on the way astronomers and astrophysicists measure the expansion of the universe in reference to the microscopic length units. A rather phenomenological trapping mechanism is assumed for the scalar field around the epoch of mini-inflation as observed, still maintaining the unmistakable behavior of the scenario stated above. Experimental searches for the scalar field, as light as ∼ 10⁻⁹ eV, as part of the dark energy, are also discussed. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

► Show Figures

Figure 1

538 KiB

Open AccessArticle

Exact Solution and Exotic Fluid in Cosmology

by Seyen Kouwn, Taeyoon Moon and Phillial Oh

Entropy 2012, 14(9), 1771-1783; https://doi.org/10.3390/e14091771 - 20 Sep 2012

Cited by 2 | Viewed by 5233

Abstract

We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only [...] Read more.

We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only one of the scalar fields is also introduced. We perform a general analysis of the ensuing cosmological equations and give various critical points and their properties. Then, we show that the model exhibits an exact cosmological solution which yields a transition from matter domination into dark energy epoch and compare it with the Λ-CDM behavior. Especially, we calculate the age of the Universe and show that it is consistent with the observational value if the equation of the state ωf of the cosmological fluid is within the range of 0.13 < ωf < 0.22. Some implication of this result is also discussed. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

► Show Figures

Figure 1

1458 KiB

Open AccessArticle

Black Holes, Cosmological Solutions, Future Singularities, and Their Thermodynamical Properties in Modified Gravity Theories

by Alvaro De la Cruz-Dombriz and Diego Sáez-Gómez

Entropy 2012, 14(9), 1717-1770; https://doi.org/10.3390/e14091717 - 18 Sep 2012

Cited by 308 | Viewed by 9153

Abstract

Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann–Lemaˆıtre–Robertson–Walker metrics. The thermodynamical properties of fourth order gravity theories are also [...] Read more.

Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann–Lemaˆıtre–Robertson–Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy–Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

► Show Figures

Figure 1

353 KiB

Open AccessArticle

Cosmology of F(T) Gravity and k-Essence

by Ratbay Myrzakulov

Entropy 2012, 14(9), 1627-1651; https://doi.org/10.3390/e14091627 - 4 Sep 2012

Cited by 40 | Viewed by 6110

Abstract

This a brief review on F(T) gravity and its relation with k-essence. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. We perform a thorough reconstruction analysis on the so-called [...] Read more.

This a brief review on F(T) gravity and its relation with k-essence. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. We perform a thorough reconstruction analysis on the so-called F(T) models, where F(T) is some general function of the torsion term, and deduce the required conditions for the equivalence between of F(T) models with pure kinetic k-essence models. We present a new class of models of F(T)-gravity and k-essence. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

314 KiB

Open AccessArticle

Stability of Accelerating Cosmology in Two Scalar-Tensor Theory: Little Rip versus de Sitter

by Yusaku Ito, Shin’ichi Nojiri and Sergei D. Odintsov

Entropy 2012, 14(8), 1578-1605; https://doi.org/10.3390/e14081578 - 23 Aug 2012

Cited by 43 | Viewed by 6138

Abstract

We develop the general reconstruction scheme in two scalar model. The quintom-like theory which may describe (different) non-singular Little Rip or de Sitter cosmology is reconstructed. The number of scalar phantom dark energy models (with Little Rip cosmology or asymptotically de Sitter evolution) [...] Read more.

We develop the general reconstruction scheme in two scalar model. The quintom-like theory which may describe (different) non-singular Little Rip or de Sitter cosmology is reconstructed. The number of scalar phantom dark energy models (with Little Rip cosmology or asymptotically de Sitter evolution) is presented. Stability issue of such dark energy cosmologies as well as the flow to fixed points are studied. The stability of Little Rip universe which leads to dissolution of bound objects sometime in future indicates that no classical transition to de Sitter space occurs. The possibility of unification of inflation with Little Rip dark energy in two scalar theory is briefly mentioned. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

► Show Figures

Figure 1

112 KiB

Open AccessArticle

A Model of Nonsingular Universe

by Changjun Gao

Entropy 2012, 14(7), 1296-1305; https://doi.org/10.3390/e14071296 - 23 Jul 2012

Cited by 11 | Viewed by 5854

Abstract

In the background of Friedmann–Robertson–Walker Universe, there exists Hawking radiation which comes from the cosmic apparent horizon due to quantum effect. Although the Hawking radiation on the late time evolution of the universe could be safely neglected, it plays an important role in [...] Read more.

In the background of Friedmann–Robertson–Walker Universe, there exists Hawking radiation which comes from the cosmic apparent horizon due to quantum effect. Although the Hawking radiation on the late time evolution of the universe could be safely neglected, it plays an important role in the very early stage of the universe. In view of this point, we identify the temperature in the scalar field potential with the Hawking temperature of cosmic apparent horizon. Then we find a nonsingular universe sourced by the temperature-dependent scalar field. We find that the universe could be created from a de Sitter phase which has the Planck energy density. Thus the Big-Bang singularity is avoided. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

► Show Figures

Figure 1

309 KiB

Open AccessArticle

The Dark Energy Properties of the Dirac–Born–Infeld Action

by Xinyou Zhang, Qing Zhang and Yongchang Huang

Entropy 2012, 14(7), 1203-1220; https://doi.org/10.3390/e14071203 - 9 Jul 2012

Cited by 2 | Viewed by 5982

Abstract

Introducing a new potential, we deduce a general Lagrangian for Dirac–Born– Infeld (DBI) inflation, in which the determinant of the induced metric naturally includes the kinetic energy and the potential energy. In particular, the potential energy and kinetic energy can convert into each [...] Read more.

Introducing a new potential, we deduce a general Lagrangian for Dirac–Born– Infeld (DBI) inflation, in which the determinant of the induced metric naturally includes the kinetic energy and the potential energy. In particular, the potential energy and kinetic energy can convert into each other at any same order, which is in agreement with the limit of classical physics. We also present a general sound speed in the evolutions of the universe, and the exact expressions of energy-momentum tensor, pressure and density. Furthermore, from the results we obtain the new equation of states. The analytic form of the action that is consistent with data turns out to be surprisingly simple and easy to categorize. Finally, we examine properties of the dark energy and introduce a novel mechanism for realizing either quintessence or phantom dark energy dominated phases within a string theoretical context. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

214 KiB

Open AccessArticle

On Chirality of the Vorticity of the Universe

by Davor Palle

Entropy 2012, 14(5), 958-965; https://doi.org/10.3390/e14050958 - 16 May 2012

Cited by 14 | Viewed by 5652

Abstract

The presence of dark energy in the Universe challenges the Einstein’s theory of gravity at cosmic scales. It motivates the inclusion of rotational degrees of freedom in the Einstein–Cartan gravity, representing the minimal and the most natural extension of the General Relativity. One [...] Read more.

The presence of dark energy in the Universe challenges the Einstein’s theory of gravity at cosmic scales. It motivates the inclusion of rotational degrees of freedom in the Einstein–Cartan gravity, representing the minimal and the most natural extension of the General Relativity. One can, consequently, expect the violation of the cosmic isotropy by the rotating Universe. We study chirality of the vorticity of the Universe within the Einstein–Cartan cosmology. The role of the spin of fermion species during the evolution of the Universe is studied by averaged spin densities and Einstein–Cartan equations. It is shown that spin density of the light Majorana neutrinos acts as a seed for vorticity at early stages of the evolution of the Universe. Its chirality can be evaluated in the vicinity of the spacelike infinity. It turns out that vorticity of the Universe has right-handed chirality. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

108 KiB

Open AccessArticle

A Phase Space Diagram for Gravity

by Xavier Hernandez

Entropy 2012, 14(5), 848-855; https://doi.org/10.3390/e14050848 - 4 May 2012

Cited by 7 | Viewed by 7822

Abstract

In modified theories of gravity including a critical acceleration scale a₀, a critical length scale r_M = (GM/a₀)^1/2 will naturally arise with the transition from the Newtonian to the dark matter mimicking regime occurring for systems larger [...] Read more.

In modified theories of gravity including a critical acceleration scale a₀, a critical length scale r_M = (GM/a₀)^1/2 will naturally arise with the transition from the Newtonian to the dark matter mimicking regime occurring for systems larger than r_M. This adds a second critical scale to gravity, in addition to the one introduced by the criterion v < c of the Schwarzschild radius, r_S= 2GM/c². The distinct dependencies of the two above length scales give rise to non-trivial phenomenology in the (mass, length) plane for astrophysical structures, which we explore here. Surprisingly, extrapolation to atomic scales suggests gravity should be at the dark matter mimicking regime there. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

► Show Figures

Figure 1

Review

Jump to: Research

216 KiB

Open AccessReview

Conformal Gravity: Dark Matter and Dark Energy

by Robert K. Nesbet

Entropy 2013, 15(1), 162-176; https://doi.org/10.3390/e15010162 - 9 Jan 2013

Cited by 24 | Viewed by 6765

Abstract

This short review examines recent progress in understanding dark matter, dark energy, and galactic halos using theory that departs minimally from standard particle physics and cosmology. Strict conformal symmetry (local Weyl scaling covariance), postulated for all elementary massless fields, retains standard fermion and [...] Read more.

This short review examines recent progress in understanding dark matter, dark energy, and galactic halos using theory that departs minimally from standard particle physics and cosmology. Strict conformal symmetry (local Weyl scaling covariance), postulated for all elementary massless fields, retains standard fermion and gauge boson theory but modifies Einstein–Hilbert general relativity and the Higgs scalar field model, with no new physical fields. Subgalactic phenomenology is retained. Without invoking dark matter, conformal gravity and a conformal Higgs model fit empirical data on galactic rotational velocities, galactic halos, and Hubble expansion including dark energy. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

316 KiB

Open AccessReview

Conformal Relativity versus Brans–Dicke and Superstring Theories

by David B. Blaschke and Mariusz P. Dąbrowski

Entropy 2012, 14(10), 1978-1996; https://doi.org/10.3390/e14101978 - 18 Oct 2012

Cited by 8 | Viewed by 6454

Abstract

We show how conformal relativity is related to Brans–Dicke theory and to low-energy-effective superstring theory. Conformal relativity or the Hoyle–Narlikar theory is invariant with respect to conformal transformations of the metric. We show that the conformal relativity action is equivalent to the transformed [...] Read more.

We show how conformal relativity is related to Brans–Dicke theory and to low-energy-effective superstring theory. Conformal relativity or the Hoyle–Narlikar theory is invariant with respect to conformal transformations of the metric. We show that the conformal relativity action is equivalent to the transformed Brans–Dicke action for ω = -3/2 (which is the border between standard scalar field and ghost) in contrast to the reduced (graviton-dilaton) low-energy-effective superstring action which corresponds to the Brans–Dicke action with ω = -1. We show that like in ekpyrotic/cyclic models, the transition through the singularity in conformal cosmology in the string frame takes place in the weak coupling regime. We also find interesting self-duality and duality relations for the graviton-dilaton actions. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

267 KiB

Open AccessReview

Exact Solutions in Modified Gravity Models

by Andrey N. Makarenko and Valery V. Obukhov

Entropy 2012, 14(7), 1140-1153; https://doi.org/10.3390/e14071140 - 25 Jun 2012

Cited by 6 | Viewed by 5594

Abstract

We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper [...] Read more.

We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

Journal Menu

Journal Browser

Modified Gravity: From Black Holes Entropy to Current Cosmology

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (17 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI