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Modified Gravity: From Black Holes Entropy to Current Cosmology

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Astrophysics, Cosmology, and Black Holes".

Deadline for manuscript submissions: closed (20 September 2012) | Viewed by 105499

Special Issue Editors

Special Issue Information

Dear Colleagues,

Recent cosmological observations strongly support that the current expansion of the universe is accelerating. The origin of such a cosmic acceleration mechanism is one of the most significant problems in modern cosmology. Indeed, this is shown by the fact that the Nobel Prize in Physics 2011 was presented to the finding of the current cosmic acceleration by means of the observations of the Type Ia supernovae.

There are two representative approaches to explain the current accelerated expansion of the universe. One is to introduce “dark energy” in the framework of general relativity. The other is to modify a gravitational theory, such as F(R) gravity, so that we can obtain so-called geometrical dark energy. It is believed that a modified gravitational theory must pass cosmological bounds and solar system tests because it corresponds to an alternative theory of gravitation to general relativity. As another meaningful touchstone of modified gravity, it is important to examine whether the second law of thermodynamics can be satisfied in the models of modified gravity.

The fundamental connection between gravitation and thermodynamics has been suggested by the discovery of black hole thermodynamics with black hole entropy and Hawking temperature. In addition, it was shown that the Einstein equation can be derived from the proportionality of the entropy to the horizon area together with the Clausius relation in thermodynamics. This consequence has been applied to various cosmological settings as well as modified gravitational theories. In particular, the connections between thermodynamics and modified gravity have recently been discussed extensively.

In this special issue, we discuss the application of thermodynamics to the test of a successful alternative gravitational theory to general relativity. Through this procedure, we can obtain a clue to resolve the dark energy problem “geometrically”. It is considered that any successful modified gravity theory should obey the second law of thermodynamics. If the second law is violated in certain universes in a model, it is more likely to be due to an incorrect generalization of the second law or some inherent inconsistency of the model itself. For the latter case, the model should be abandoned. It is strongly expected that the considerations of this special issue can produce our new physical understanding on entropy in the context of the relation between thermodynamics and gravitation and shed light on novel ingredients as well as insights on modern cosmology, in particular new properties of dark energy.

Prof. Dr. Sergei D. Odintsov
Dr. Kazuharu Bamba
Guest Editors

 

Keywords

  • Quantum aspects of black holes, evaporation, thermodynamics
  • Black hole entropy
  • Modified theories of gravity
  • Dark energy
  • Cosmology

Published Papers (17 papers)

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Research

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147 KiB  
Article
The Thermal Entropy Density of Spacetime
by Rongjia Yang
Entropy 2013, 15(1), 156-161; https://doi.org/10.3390/e15010156 - 08 Jan 2013
Cited by 9 | Viewed by 6782
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  
Article
Entropy and Gravity
by Øyvind Grøn
Entropy 2012, 14(12), 2456-2477; https://doi.org/10.3390/e14122456 - 04 Dec 2012
Cited by 15 | Viewed by 8434
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)
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195 KiB  
Article
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 5952
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)
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193 KiB  
Article
Viscosity in Modified Gravity
by Iver Brevik
Entropy 2012, 14(11), 2302-2310; https://doi.org/10.3390/e14112302 - 12 Nov 2012
Cited by 10 | Viewed by 4916
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  
Article
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 - 02 Nov 2012
Cited by 72 | Viewed by 5228
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  
Article
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 6884
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, Λobs ∼ 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, Λobs 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)
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538 KiB  
Article
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 4943
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)
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1458 KiB  
Article
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 295 | Viewed by 8495
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)
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353 KiB  
Article
Cosmology of F(T) Gravity and k-Essence
by Ratbay Myrzakulov
Entropy 2012, 14(9), 1627-1651; https://doi.org/10.3390/e14091627 - 04 Sep 2012
Cited by 38 | Viewed by 5800
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  
Article
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 5707
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)
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112 KiB  
Article
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 5480
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)
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309 KiB  
Article
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 - 09 Jul 2012
Cited by 40 | Viewed by 5591
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  
Article
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 5386
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  
Article
A Phase Space Diagram for Gravity
by Xavier Hernandez
Entropy 2012, 14(5), 848-855; https://doi.org/10.3390/e14050848 - 04 May 2012
Cited by 6 | Viewed by 7412
Abstract
In modified theories of gravity including a critical acceleration scale a0, a critical length scale rM = (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 rM = (GM/a0)1/2 will naturally arise with the transition from the Newtonian to the dark matter mimicking regime occurring for systems larger than rM. This adds a second critical scale to gravity, in addition to the one introduced by the criterion v < c of the Schwarzschild radius, rS = 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)
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Review

Jump to: Research

216 KiB  
Review
Conformal Gravity: Dark Matter and Dark Energy
by Robert K. Nesbet
Entropy 2013, 15(1), 162-176; https://doi.org/10.3390/e15010162 - 09 Jan 2013
Cited by 24 | Viewed by 6153
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  
Review
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 6 | Viewed by 6040
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  
Review
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 5277
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)
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