The Friedmann equations of general relativity can be derived from the first law of thermodynamics when the entropy of the apparent horizon of a spatially isotropic universe is given by the Bekenstein-Hawking entropy. We point out that if the entropy of the apparent horizon receives a logarithmic correction, the first law of thermodynamics leads to a modified Friedmann equation which corresponds precisely to the time-time component of the semi-classical Einstein field equations sourced by the trace anomaly of ${\cal{N}}=4$ U(N) super-Yang-Mills theory. This correspondence allows for a thermodynamic description of the dynamics of the Randall-Sundrum braneworld scenario.
Holonomy corrections to scalar perturbations are investigated in the loop quantum cosmology framework. Due to the effective approach, modifications of the algebra of constraints generically lead to anomalies. In order to remove those anomalies, counter-terms are introduced. We find a way to explicitly fulfill the conditions for anomaly freedom and we give explicit expressions for the counter-terms. Surprisingly, the "new quantization scheme" naturally arises in this procedure. The gauge invariant variables are found and equations of motion for the anomaly-free scalar perturbations are derived.…
We investigate vector perturbations with holonomy corrections in the framework of loop quantum cosmology. Conditions to achieve anomaly freedom for these perturbations are found at all orders. This requires the introduction of counter-terms in the hamiltonian constraint. We also show that anomaly freedom requires the diffeomorphism constraint to hold its classical form when scalar matter is added although the issue of a vector matter source, required for full consistency, remains to be investigated. The gauge-invariant variable and the corresponding equation of motion are derived. The propagat…
This article addresses the issue of the closure of the algebra of constraints for generic (cosmological) perturbations when taking into account simultaneously the two main corrections of effective loop quantum cosmology, namely the holonomy and the inverse-volume terms. Previous works on either the holonomy or the inverse volume case are reviewed and generalized. In the inverse-volume case, we point out new possibilities. An anomaly-free solution including both corrections is found for perturbations, and the corresponding equations of motion are derived.
The area of a future holographic screen increases monotonically. Associating this area with entropy results in a generalized second law for Cosmology (GSLC). Unlike black hole horizons, screens relevant to Cosmology have no thermodynamical interpretation. We suggest relating the entropy of the screens to spacetime degrees of freedom surface density derived from a (seemingly) phase space. This construction enables us to identify the entropy of any holographic screen as the entropy detected by accelerating observers due to their acceleration. Using Unruh's temperature and the equivalence princip…
We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a non-trivial minimum. For theories with dilatation anomaly one needs as a non-trivial "cosmon condition" that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short-distance renormalization group behavior of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible.
It is shown that the Pioneer anomaly is a natural consequence of variable speed of light cosmological models wherein the speed of light is assumed to be a power-law function of the scale factor (or cosmic time). In other words, the Pioneer anomaly can be regarded as a non-gravitational effect of the continuously decreasing speed of light which indicates itself as an anomalous light propagation time delay in local frames. This time delay is accordingly interpreted as an additional Doppler blue shift.
In the spatially flat case of loop quantum cosmology, the connection $\bar{k}$ is usually replaced by the holonomy $\frac{\sin(\barμk)}{\barμ}$ in the effective theory. In this paper, instead of the $\barμ$ scheme, we use a generalised, undertermined function $g(\bar{k},\bar{p})$ to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction on the form of $g(\bar{k},\bar{p})$, then we derive the gauge invariant equations of motion of the scalar, tensor and vector perturbations and study the inflat…
The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects at macroscopic scales. In an effective field theory approach, the effective action of the anomaly is an infrared relevant term that should be added to the Einstein-Hilbert action of classical General Relativity to take account of macroscop…
In this paper, we study thermodynamical properties of the apparent horizon in a universe governed by quasi-topological gravity. Our aim is twofold. First, by using the variational method we derive the general form of Friedmann equation in quasi-topological gravity. Then, by applying the first law of thermodynamics on the apparent horizon, after using the entropy expression associated with the black hole horizon in quasi-topological gravity, and replacing the horizon radius, $r_{+}$, with the apparent horizon radius, $\tilde{r}_{A}$, we derive the corresponding Friedmann equation in quasi-topol…
We present exact analytical black hole solutions with conformal anomaly in AdS space and discuss the thermodynamical properties of these black hole solutions. These black holes can have a positive, zero and negative constant curvature horizon, respectively. For the black hole with a positive constant curvature horizon, there exists a minimal horizon determined by the coefficient of the trace anomaly, the black hole with a smaller horizon is thermodynamically unstable, while it is stable for the case with a larger horizon. The Hawking-Page transition happens in this case. For the black hole wit…
The aim here is to provide a set of equations for cosmology in terms of information and thermodynamical parameters. The method we implement in order to describe the universe is a development of Padmanabhan\rq{}s approach which is based on the fact that emergence of the cosmic space is provided by the evolution of the cosmic time. In this line we obtain the Friedmann equation or its equivalent the conservation law in terms of information by the implementation of Laundauer\rq{}s principle or in other words the information loss/production rate. Hence, a self consistent description of the universe…
Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive cosmological model proposed lately, the corrected entropic formula of the apparent horizon is obtained with the help of the modified Friedmann equations. This entropy-area relation, together with the identified internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation $δQ=T dS$, the modified Fri…
An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential $e$-folds could be very large, before the transition to the unstable version and the beginning of the Starobinsky inflation. Thus, the stable exponential expansion can be seen as a pre-inflationary semiclassical cosmological solution. We explore whether this stable phase could follow after the bounce, subsequent to the contraction of the Universe. Extending the previous consideration of the bounce, w…
This work is to study the generalized second law (GSL) of thermodynamics in tachyon cosmology where the boundary of the universe is assumed to be enclosed by a dynamical apparent horizon. The model is constrained with the observational data. The two logarithmic and power law corrected entropy is also discussed and conditions to validate the GSL and corrected entropies are obtained.
Black holes have been a subject of investigation over years not only because they have interesting physical properties, but also because they seem to be the appropriate tool for studying gravity in quantum scale. Although a lot of effort has been made to understand the aspects of spacetime on the quantum scale, the approach which includes noncommutativity of spacetime proves to be promising among several possibilities. In this paper, we use the Hamilton-Jacobi method to study the thermodynamic properties of cylindrical black holes (black strings) in noncommutative spacetime. It is also investi…
The thermodynamic properties of loop quantum cosmology (LQC) without considering the Lorentz term were established in \cite{Zhu09}. In this paper, we extend this result to the recent proposed new model of LQC with the Lorentz term. We investigate the thermodynamics of LQC on the apparent horizon of the Friedmann-Lematre-Robertson-Walker universe. The result shows that the effective density and effective pressure in the modified Friedmann equation of LQC not only determines the evolution of the universe but can also serve as the thermodynamic quantities. Moreover, with the help of the Misner-Sh…
We derive non-flat cosmological models for two cases (i.e., dust and radiation) in the context of Møller's tetradic theory (MTT) of gravitation using the tetrad that creates the non-flat Friedmann-Robertson-Walker (FRW) metric. These two models are affected by the free dimensional parameter, $λ$, that characterized MTT, which approaches zero in the flat case for both models. Using standard definitions of thermodynamics, we calculate the radius horizon, Hawking temperature, and entropy of our non-flat models in the framework of cosmology and show the effect of $λ$ on open and closed universes. …
We review the fundamental results of a new cosmological model, based on conformal gravity, and apply them to the analysis of the early data of the Pioneer anomaly. We show that our conformal cosmology can naturally explain the anomalous acceleration of the Pioneer 10 and 11 spacecraft, in terms of a local blueshift region extending around the solar system and therefore affecting the frequencies of the navigational radio signals exchanged between Earth and the spacecraft. On the contrary, conformal gravity corrections alone would not be able to account for dynamical effects of such magnitude to…
Brans-Dicke cosmological models for a spatially isotropic and homogeneous universe are tested in terms of the validity of the Generalized Second Law of Thermodynamics (GSL). The investigation is carried out in the Einstein frame. It is found that the models are thermodynamically viable for negative values of the Brans-Dicke parameter w and thus are quite consistent with the recent accelerated expansion of the universe.
We show that there is a correspondence between cosmology from non-extensive thermodynamics and cosmology with fluids of redefined and generalized equation of state. We first establish the correspondence in the case of basic non-extensive thermodynamics, and then we proceed by investigating the more consistent case, from the quantum field theoretical point of view, of varying exponent, namely depending on the scale. The obtained duality provides a way of explaining the complicated phenomenological forms of the effective fluid equation-of-state parameters that are being broadly used in the liter…
We describe the evolution of the early and late universe from thermodynamic considerations, using the generalized non-extensive Tsallis entropy with a variable exponent. A new element in our analysis is the inclusion of a bulk viscosity in the description of the cosmic fluid. Using the generalized Friedmann equation, a description of the early and the late universe is obtained.
We investigate the validity of the generalized second law of gravitational thermodynamics on the apparent and event horizons in a non-flat FRW universe containing the interacting dark energy with dark matter. We show that for the dynamical apparent horizon, the generalized second law is always satisfied throughout the history of the universe for any spatial curvature and it is independent of the equation of state parameter of the interacting dark energy model. Whereas for the cosmological event horizon, the validity of the generalized second law depends on the equation of state parameter of th…
Using the corrected entropy-area relation motivated by the loop quantum gravity, we investigate the validity of the generalized second law of thermodynamics in the framework of modified FRW cosmology. We consider a non-flat universe filled with an interacting viscous dark energy with dark matter and radiation. The boundary of the universe is assumed to be the dynamical apparent horizon. We find out that the generalized second law is always satisfied throughout the history of the universe for any spatial curvature regardless of the dark energy model.
A new thermodynamics of scalar-tensor gravity is applied to spatially homogeneous and isotropic cosmologies in this class of theories and tested on analytical solutions. A forever-expanding universe approaches the Einstein "state of equilibrium" with zero effective temperature at late times and departs from it near spacetime singularities. "Cooling" by expansion and "heating" by singularities compete near the Big Rip, where it is found that the effective temperature diverges in the case of a conformally coupled scalar field.
We construct cosmological solutions of higher spin gravity in 2+1 dimensional de Sitter space. We show that a consistent thermodynamics can be obtained for their horizons by demanding appropriate holonomy conditions. This is equivalent to demanding the integrability of the Euclidean boundary CFT partition function, and reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By using a prescription of Maldacena, we relate the thermodynamics of these solutions to those of higher spin black holes in AdS_3.
The cosmological Friedmann equation sourced by the trace anomaly of a conformal field theory that is dual to the five-dimensional Schwarzschild-AdS geometry can be derived from the first law of thermodynamics if the apparent horizon of the boundary spacetime acquires a logarithmically-corrected Bekenstein-Hawking entropy. It is shown that such a correction to the entropy can arise when the generalized uncertainty principle (GUP) is invoked. The necessary condition for such a thermodynamic derivation directly relates the GUP parameter to the conformal anomaly. It is consistent with the existenc…
By dropping particles into black hole, we have employed the recently new assumption [1] that the change of the black hole mass(enthalpy) should be the same amount as the energy of an infalling particle($ω= dM$), to carefully test the laws of thermodynamics and the weak cosmic censorship conjecture of a conformal anomaly corrected AdS black hole in different phase spaces. Using the energy-momentum relation, the result shows that the first law, second law and weak cosmic censorship conjecture of black hole are all valid in the normal phase space, no violations occur. In the extended phase space,…
We analyze the thermodynamical consistency of entropic-force cosmological models. Our analysis is based on a generalized entropy scaling with an arbitrary power of the Hubble radius. The Bekenstein-Hawking entropy, proportional to the area, and the nonadditive $S_{δ=3/2}$-entropy, proportional to the volume, are particular cases. One of the points to be solved by entropic-force cosmology for being taken as a serious alternative to mainstream cosmology is to provide a physical principle that points out what entropy and temperature have to be used. We determine the temperature of the universe ho…
In this paper, the generalized second law (GSL) of thermodynamics and entropy is revisited in the context of cosmological models with bouncing behavior such as chameleon cosmology where the boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. From a thermodynamic point of view, to link between thermodynamic and geometric parameters in cosmological models, we introduce "entropy rate of change multiplied by the temperature" as a model independent thermodynamic state parameter together with the well known $\{r,s \}$ statefinder to differentiate the dark energy mod…
Considering an arbitrary, varying equation of the state parameter, the thermodynamic properties of the dark energy fluid in a semiclassical loop quantum cosmology scenario, which we consider the inverse volume modification, is studied. The equation of the state parameters are corrected as a semiclassical one during considering the effective behavior. Assuming that the apparent horizon has Hawking temperature, the modified entropy-area relation is obtained, we find that this relation is different from the one which is obtained by considering the holonomy correction. Considering the dark energy …
Entropy applications in cosmology: spacetime thermodynamics, holographic dark energy, entropic gravity and beyond - a review
National Observatory of Athens（雅典国家天文台）；University of Science and Technology of China（中国科学技术大学）；Universidad Católica del Norte（北方天主教大学）；University of Lleida（莱里达大学）；University of Patras（帕特雷大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；University of Waterloo（滑铁卢大学）
This paper is devoted to investigate the thermodynamic stability of a generic cosmological fluid known as Van der Waals fluid in the context of flat FRW universe. It is treated as a perfect fluid that obeys the equation of state $P=\frac{γρ}{1-βρ}-αρ^{2}, 0\leqγ<1$, where $ρ$ stands for energy density and $P$ stands for pressure of the fluid. In this regard, we discuss the behavior of physical parameters to analyze the evolution of the universe. We investigate whether the cosmological scenario fulfills the third law of thermodynamics using specific heat formalism. Next we discuss the thermal e…
Recently, we have investigated the dynamics of the universe in tachyon cosmology with non-minimal coupling to matter \cite{faraj}-\cite{faraj3}. In particular, for the interacting holographic dark energy (IHDE), the model is studied in \cite{Ravanpak}. In the current work, a significant observational program has been conducted to unveil the model's thermodynamic properties. Our result shows that the IHDE version of our model better fits the observational data than $Λ$CDM model. The first and generalized second thermodynamics laws for the universe enveloped by cosmological apparent and event ho…
In this paper we have studied Van-Der-Waals fluid system with the generalized EOS as as discussed in the recent works of Kremer, G.M [1, 4], Vardiashvili, G [2], Jantsch, R.C [3], Capozziello, S [5]. and are functions of energy density and time that are different for the three types of Van der Waals fluid which are one parameter model, two parameters model and three parameters model. We have studied the changes in the parameters for different cosmic phases. We have also investigated the thermodynamics and the stability conditions for these three models. Finally, we have resolved the finite tim…
Reconstruction of f(G) Gravity from an Interacting Viscous Generalized QCD Ghost Dark Energy Model: Cosmology and Thermodynamics: Cosmology and Thermodynamics
Mukhtar Auezov South Kazakhstan University（穆赫塔尔·阿尤佐夫南哈萨克斯坦大学）；Amity University Kolkata（阿米提大学加尔各答分校）；L.N. Gumilyov Eurasian National University（L.N. 古米廖夫欧亚国立大学）
We investigate the validity of the generalized second law of thermodynamics in a universe governed by Horava-Lifshitz gravity. Under the equilibrium assumption, that is in the late-time cosmological regime, we calculate separately the entropy time-variation for the matter fluid and, using the modified entropy relation, that of the apparent horizon itself. We find that under detailed balance the generalized second law is generally valid for flat and closed geometry and it is conditionally valid for an open universe, while beyond detailed balance it is only conditionally valid for all curvatures…
We discuss the evolution of the universe in the context of the second law of thermodynamics from its early stages to the far future. Cosmological observations suggest that most matter and radiation will be absorbed by the cosmological horizon. On the local scale, the matter that is not ejected from our supercluster will collapse to a supermassive black hole and then slowly evaporate. The history of the universe is that of an approach to the equilibrium state of the gravitational field.
We apply the first law of thermodynamics to the apparent horizon of the universe with the power-law corrected and non-extensive Tsallis entropies rather than the Bekenstein-Hawking one. We examine the cosmological properties in the two entropy models by using the CosmoMC package. In particular, the first numerical study for the cosmological observables with the power-law corrected entropy is performed. We also show that the neutrino mass sum has a non-zero central value with a relaxed upper bound in the Tsallis entropy model comparing with that in the $Λ$CDM one.
We construct modified cosmological scenarios through the application of the first law of thermodynamics in the universe horizon, but using the generalized, nonextensive Tsallis entropy instead of the usual Bekenstein-Hawking one. We result to modified cosmological equations that possess the usual ones as a particular limit, but which in the general case contain extra terms that appear for the first time, that constitute an effective dark energy sector quantified by the nonextensive parameter $δ$. When the matter sector is dust, we extract analytical expressions for the dark energy density and …
