Study of Thermodynamic Quantities in Generalized Gravity Theories (original) (raw)
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Modified gravity and cosmology
Physics Reports, 2012
In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f (R), general higher-order theories, Hořava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.
Higher-order gravity and the cosmological background of gravitational waves
Astroparticle Physics, 2008
The cosmological background of gravitational waves can be tuned by the higher-order corrections to the gravitational Lagrangian. In particular, it can be shown that assuming R 1+ǫ , where ǫ indicates a generic (eventually small) correction to the Hilbert-Einstein action in the Ricci scalar R, gives a parametric approach to control the evolution and the production mechanism of gravitational waves in the early Universe.
2010
We propose the most general modified first-order Ho\v{r}ava-Lifshitz (HL) gravity, whose action does not contain time derivatives higher than the second order. The Hamiltonian structure of this theory is studied in all the details in the case of the spatially-flat FRW space-time, demonstrating many of the features of the general theory. It is shown that, with some plausible assumptions, including the projectability of the lapse function, this model is consistent. As a large class of such theories, the modified HL F(R)F(R)F(R) gravity is introduced. The study of its ultraviolet properties shows that its z=3z=3z=3 version seems to be renormalizable in the same way as the original HL proposal. The Hamiltonian analysis of the modified HL F(R)F(R)F(R) gravity shows that it is in general a consistent theory. The F(R)F(R)F(R) gravity action is also studied in the fixed-gauge form, where the appearance of a scalar field is particularly illustrative. Then the spatially-flat FRW cosmology for this F(R)F(R)F(R) gravity is investigated. It is shown that a special choice of parameters for this theory leads to the same equations of motion as in the case of traditional F(R)F(R)F(R) gravity. Nevertheless, the cosmological structure of the modified HL F(R)F(R)F(R) gravity turns out to be much richer than for its traditional counterpart. The emergence of multiple de Sitter solutions indicates to the possibility of unification of early-time inflation with late-time acceleration within the same model. Power-law F(R)F(R)F(R) theories are investigated in detail. It is analytically shown that they have a quite rich cosmological structure: early/late-time cosmic acceleration of quintessence, as well as of phantom types. Also it is demonstrated that all the four known types of finite-time future singularities may occur in the power-law HL F(R)F(R)F(R) gravity. Finally, a covariant proposal for (renormalizable) F(R)F(R)F(R) gravity within the HL spirit is presented.
Unifying inflation with dark energy in modified F(R) Hořava–Lifshitz gravity
The European Physical Journal C, 2010
We study FRW cosmology for a non-linear modified F (R) Hořava-Lifshitz gravity which has a viable convenient counterpart. A unified description of early-time inflation and late-time acceleration is possible in this theory, but the cosmological dynamic details are generically different from the ones of the convenient viable F (R) model. Remarkably, for some specific choice of parameters they do coincide. The emergence of finite-time future singularities is investigated in detail. It is shown that these singularities can be cured by adding an extra, higher-derivative term, which turns out to be qualitatively different when compared with the corresponding one of the convenient F (R) theory.
Physical Review D, 2010
We propose the most general modified first-order Hořava-Lifshitz gravity, whose action does not contain time derivatives higher than the second order. The Hamiltonian structure of this theory is studied in all the details in the case of the spatially-flat FRW space-time, demonstrating many of the features of the general theory. It is shown that, with some plausible assumptions, including the projectability of the lapse function, this model is consistent. As a large class of such theories, the modified Hořava-Lifshitz F (R) gravity is introduced. The study of its ultraviolet properties shows that its z = 3 version seems to be renormalizable in the same way as the original Hořava-Lifshitz proposal. The Hamiltonian analysis of the modified Hořava-Lifshitz F (R) gravity shows that it is in general a consistent theory. The F (R) gravity action is also studied in the fixed-gauge form, where the appearance of a scalar field is particularly illustrative. Then the spatially-flat FRW cosmology for this F (R) gravity is investigated. It is shown that a special choice of parameters for this theory leads to the same equations of motion as in the case of traditional F (R) gravity. Nevertheless, the cosmological structure of the modified Hořava-Lifshitz F (R) gravity turns out to be much richer than for its traditional counterpart. The emergence of multiple de Sitter solutions indicates to the possibility of unification of early-time inflation with late-time acceleration within the same model. Power-law F (R) theories are also investigated in detail. It is analytically shown that they have a quite rich cosmological structure: early/late-time cosmic acceleration of quintessence, as well as of phantom types. Also it is demonstrated that all the four known types of finite-time future singularities may occur in the power-law Hořava-Lifshitz F (R) gravity. Finally, a covariant proposal for (renormalizable) F (R) gravity within the Hořava-Lifshitz spirit is presented.
Thermal evolution of f(R) modified gravity in the frame of S − M Holographic Dark Energy model
2020
In this work we establish the main cosmological parameters namely the deceleration parameter q, the equation of state parameter w and the diagnostic omega Om for f (R) modified gravity using Sharma-Mitall (S−M) Holographic Dark Energy model (SMHDE). Our model shows a type of stability is achieved by studying the behavior of the square speed of sound parameter which has a positive behavior over the given range. For the considered red shift z range, we study the evolution of energy conditions for our model and the growth of dark energy. The results fit the observations that the dark energy increase with time and the universe has an accelerated expansion epoch. Thermal analysis is considered through the quantum correction for power law and logarithmic entropy, consequently we study the validity of the generalized second law of thermodynamics the results show that the generalized second law of thermodynamics holds using power law corrected scenario.
Gravity in the Context of Dark Energy with Power Law Expansion and Energy Conditions*
Chinese Physics C
The objective of this work is to generate a general formalism of gravity in the context of dark energy under the framework of K-essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where is the familiar Ricci scalar, is the DBI type non-canonical Lagrangian with , and ϕ is the K-essence scalar field. The emergent gravity metric ( ) and the well known gravitational metric ( ) are not conformally equivalent. We have constructed a modified field equation using the metric formalism in -gravity incorporating the corresponding Friedmann equations into the framework of the background gravitational metric, which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of the modified Friedmann equations have been deduced for the specific choice of , which is of Starobinsky-type, using the power law expansion method. The consistency of the model with the accelerating phase of the universe has been shown when we restrict ourselves to consider the value of t...
Dark Energy Problem, Physics of Early Universe and Some New Approaches in Gravity
Entropy, 2012
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.
International Journal of Advanced Science and Engineering, 2019
In the present study, we have accounted for the accelerated expansion of the universe in the framework of the generalized Brans-Dicke theory. It has been shown very clearly that the transition of the universe from a phase of deceleration to that of acceleration can be explained by the generalized Brans-Dicke theory, without having to consider any contribution from the entity called dark energy. The present model shows a signature flip of the deceleration parameter, from a positive to a negative value, occurring in the recent past of the matter dominated era. We have determined the functional form of the Brans-Dicke parameter, expressed in terms of the scalar field. This functional form causes the effective pressure to be sufficiently negative to drive the accelerated expansion of the universe. It has been found in the present study that the gravitational constant increases with time. 1. INTODUCTION It has been established beyond doubt, by recent astrophysical observations, that there was a smooth transition of the universe from a decelerated phase to an accelerated phase of expansion [1, 2]. The reason behind this accelerated expansion has been a matter of intense research for many years. It is known to us that normal matter interacts through the gravitational force and it has a positive definite density and pressure. Therefore, there must be some other kind of matter responsible for the accelerated expansion, which makes the effective pressure sufficiently negative, causing a repulsive effect. This new entity is generally referred to as dark energy. In the past few years a lot of research has been undertaken to analyse the nature of this new form of energy, responsible for accelerated expansion. A number of models have been proposed so far to account for the acceleration of the universe. The true composition and behaviour of this new entity is yet to be determined. The most obvious choice to represent dark energy has been the cosmological constant, denoted by the symbol Λ (lambda) [3]. But there are serious problems regarding the value of this constant which can't be accurately determined by the ΛCDM model. The value of Λ, obtained from recent observations for an accelerating universe, is not consistent with the value in Planck scale or Electro-weak scale [4]. By constructing a model, where Λ is a function of time, this problem can be partly solved. Several such models have been formulated but they have their own shortcomings [5, 6]. Scalar field models have been proposed as an alternative to the dynamical Λ models. Here, the equation of state of dark energy is a function of time. Quintessence models were proposed as one of the most important types among the scalar field models. These models have a potential function V(), enabling the pressure sector, which is a function of the scalar field, to have a sufficiently large negative value, leading to the predictions consistent with observations regarding the accelerated expansion of the universe [7, 8]. A major limitation of these quintessence models is that most of the quintessence potentials are arbitrarily chosen, without having any theoretical basis behind their formulation. Quite naturally, a large number of models, based on scalar fields, such as the tachyon, k-essence, holographic dark energy models have come into existence with their strengths and limitations [9, 10, 11]. The cold dark matter and dark energy are normally allowed to evolve independently in most of the scalar field models. There are some studies where one of them decays into the other through some interaction between them [12]. A non-minimal coupling of the scalar field with the dark matter sector, through an interference term in the action, has helped us to explain the accelerated expansion of the universe. These are known as chameleon fields and they can effectively serve as dark energy, causing the cosmic acceleration [13, 14]. In the framework of Brans-Dicke (BD) theory, non-minimal coupling between the scalar field and geometry, play a very important role in explaining the observed acceleration. A self-interaction potential (), which is a function of the BD scalar field , has often been incorporated in the framework of Brans-Dicke theory to explain the cosmic acceleration [15]. In some cosmological models, a quintessence scalar field is introduced in
Dilaton Dark Energy Model in f(R), f(T) and Hořava-Lifshitz Gravities
International Journal of Theoretical Physics, 2011
In this work, we have considered dilaton dark energy model in Weyl-scaled induced gravitational theory in presence of barotropic fluid. It is to be noted that the dilaton field behaves as a quintessence. Here we have discussed the role of dilaton dark energy in modified gravity theories namely, f (R), f (T) and Hořava-Lifshitz gravities and analyzed the behaviour of the dilaton field and the corresponding potential in respect to these modified gravity theories instead of Einstein's gravity. In f (R) and f (T) gravities, we have considered some particular forms of f (R) and f (T) and we have shown that the potentials always increase with the dilaton fields. But in Hořava-Lifshitz gravity, it has been seen that the potential always decreases as dilation field increases.