Modified Friedmann Equations from Tsallis Entropy

It was shown by Tsallis and Cirto that thermodynamical entropy of a gravitational system such as black hole must be generalized to the non-additive entropy, which is given by $S_h=\gamma A^{\beta}$, where $A$ is the horizon area and $\beta$ is the nonextensive parameter \cite{Tsa}. In this paper, by taking the entropy associated with the apparent horizon of the Friedmann-Robertson-Walker (FRW) Universe in the form of Tsallis entropy, and assuming the first law of thermodynamics, $dE=T_hdS_h+WdV$, holds on the apparent horizon, we are able to derive the corresponding Friedmann equations describing the dynamics of the universe with any spatial curvature. We also examine the time evolution of the total entropy and show that the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon. Then, modifying the emergence proposal of gravity proposed by Padmanabhan and calculating the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space, we again arrive at the modified Friedmann equation of the FRW Universe with any spatial curvature which is the same as one obtained from the first law of thermodynamics. We also study the cosmological consequences of Tsallis cosmology. Interestingly enough, we find that this model can explain simultaneously the late time acceleration in the universe filled with pressureless matter without invoking dark energy, as well as the early deceleration. Besides, the age problem can be circumvented automatically for an accelerated universe and is estimated larger than $3/2$ age of the universe in standard cosmology. For $\beta=2/5$, we find $13.12$ Gyr $< t_0 < 16.32$ Gyr, which is consistent with recent observations. We also comment on the density perturbation in the context of Tsallis cosmology.Comment: 11 pages, two columns. A new section regarding the cosmological consequences of this model was added. Also text was revised and new references adde

Entropic Corrections to Friedmann Equations

Recently, Verlinde discussed that gravity can be understood as an entropic force caused by changes in the information associated with the positions of material bodies. In the Verlinde's argument, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. In this note, by employing this modified entropy-area relation, we derive corrections to Newton's law of gravitation as well as modified Friedman equations by adopting the viewpoint that gravity can be emerged as an entropic force. Our study further supports the universality of the log correction and provides a strong consistency check on Verlinde's model.Comment: 4 pages, the version appears in Phys. Rev.

Interacting holographic dark energy in Brans-Dicke theory

We study cosmological application of interacting holographic energy density in the framework of Brans-Dicke cosmology. We obtain the equation of state and the deceleration parameter of the holographic dark energy in a non-flat universe. As system's IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as $L=ar(t)$. We find that the combination of Brans-Dicke field and holographic dark energy can accommodate $w_D = -1$ crossing for the equation of state of \textit{noninteracting} holographic dark energy. When an interaction between dark energy and dark matter is taken into account, the transition of $w_D$ to phantom regime can be more easily accounted for than when resort to the Einstein field equations is made.Comment: 13 pages, new version, to appear in Phys. Lett.

Interacting new agegraphic dark energy in non-flat Brans-Dicke cosmology

We construct a cosmological model of late acceleration based on the new agegraphic dark energy model in the framework of Brans-Dicke cosmology where the new agegraphic energy density $\rho_{D}= 3n^2 m^2_p /\eta^{2}$ is replaced with $\rho_{D}= {3n^2\phi^2}/({4\omega \eta^2}$). We show that the combination of Brans-Dicke field and agegraphic dark energy can accommodate $w_D = -1$ crossing for the equation of state of \textit{noninteracting} dark energy. When an interaction between dark energy and dark matter is taken into account, the transition of $w_D$ to phantom regime can be more easily accounted for than when resort to the Einstein field equations is made. In the limiting case $\alpha = 0$ $(\omega\to \infty)$, all previous results of the new agegraphic dark energy in Einstein gravity are restored.Comment: 9 pages. The version to appear in Phys. Rev.

Holographic Scalar Fields Models of Dark Energy

Many theoretical attempts toward reconstructing the potential and dynamics of the scalar fields have been done in the literature by establishing a connection between holographic/agegraphic energy density and a scalar field model of dark energy. However, in most of these cases the analytical form of the potentials in terms of the scalar field have not been reconstructed due to the complexity of the equations involved. In this paper, by taking Hubble radius as system's IR cutoff, we are able to reconstruct the analytical form of the potentials as a function of scalar field, namely $V=V(\phi)$ as well as the dynamics of the scalar fields as a function of time, namely $\phi=\phi(t)$ by establishing the correspondence between holographic energy density and quintessence, tachyon, K-essence and dilaton energy density in a flat FRW universe. The reconstructed potentials are quite reasonable and have scaling solutions. Our study further supports the viability of the holographic dark energy model with Hubble radius as IR cutoff.Comment: 6 pages, accepted by Phys. Rev.

Thermodynamics of interacting holographic dark energy with apparent horizon as an IR cutoff

As soon as an interaction between holographic dark energy and dark matter is taken into account, the identification of IR cutoff with Hubble radius $H^{-1}$, in flat universe, can simultaneously drive accelerated expansion and solve the coincidence problem. Based on this, we demonstrate that in a non-flat universe the natural choice for IR cutoff could be the apparent horizon radius, $\tilde{r}_A={1}/{\sqrt{H^2+k/a^2}}$. We show that any interaction of dark matter with holographic dark energy, whose infrared cutoff is set by the apparent horizon radius, implies an accelerated expansion and a constant ratio of the energy densities of both components thus solving the coincidence problem. We also verify that for a universe filled with dark energy and dark matter the Friedmann equation can be written in the form of the modified first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent horizon. In addition, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon. These results hold regardless of the specific form of dark energy and interaction term. Our study might reveal that in an accelerating universe with spatial curvature, the apparent horizon is a physical boundary from the thermodynamical point of view.Comment: 11 pages, Accepted in Class. Quantum. Gra

Higher dimensional charged f(R)f(R) black holes

We construct a new class of higher dimensional black hole solutions of $f(R)$ theory coupled to a nonlinear Maxwell field. In deriving these solutions the traceless property of the energy-momentum tensor of the matter filed plays a crucial role. In $n$-dimensional spacetime the energy-momentum tensor of conformally invariant Maxwell field is traceless provided we take $n=4p$, where $p$ is the power of conformally invariant Maxwell lagrangian. These black hole solutions are similar to higher dimensional Reissner-Nordstrom AdS black holes but only exist for dimensions which are multiples of four. We calculate the conserved and thermodynamic quantities of these black holes and check the validity of the first law of black hole thermodynamics by computing a Smarr-type formula for the total mass of the solutions. Finally, we study the local stability of the solutions and find that there is indeed a phase transition for higher dimensional $f(R)$ black holes with conformally invariant Maxwell source.Comment: 13 pages, 7 figure

Thermodynamics of the apparent horizon in infrared modified Horava-Lifshitz gravity

It is well known that by applying the first law of thermodynamics to the apparent horizon of a Friedmann-Robertson-Walker universe, one can derive the corresponding Friedmann equations in Einstein, Gauss-Bonnet, and more general Lovelock gravity. Is this a generic feature of any gravitational theory? Is the prescription applicable to other gravities? In this paper we would like to address the above questions by examining the same procedure for Horava-Lifshitz gravity. We find that in Horava-Lifshitz gravity, this approach does not work and we fail to reproduce a corresponding Friedmann equation in this theory by applying the first law of thermodynamics on the apparent horizon, together with the appropriate expression for the entropy in Horava-Lifshitz gravity. The reason for this failure seems to be due to the fact that Horava-Lifshitz gravity is not diffeomorphism invariant, and thus, the corresponding field equation cannot be derived from the first law around horizon in the spacetime. Without this, it implies that the specific gravitational theory is not consistent, which shows an additional problematic feature of Horrava-Lifshitz gravity. Nevertheless, if we still take the area formula of geometric entropy and regard Horava-Lifshitz sector in the Friedmann equation as an effective dark radiation, we are able to extract the corresponding Friedmann equation from the first law of thermodynamics.Comment: 9 pages, the abstract, introduction and conclusions of the text were revised to remove text overlap with arXiv:hep-th/0602156 by other author

Thermodynamics of charged topological dilaton black holes

A class of $(n+1)$-dimensional topological black hole solutions in Einstein-Maxwell-dilaton theory with Liouville-type potentials for the dilaton field is presented. In these spacetimes, black hole horizon and cosmological horizon can be an $(n-1)$-dimensional positive, zero or negative constant curvature hypersurface. Because of the presence of the dilaton field, these topological black holes are neither asymptotically flat nor (anti)-de Sitter. We calculate the charge, mass, temperature, entropy and electric potential of these solutions. We also analyze thermodynamics of these topological black holes and disclose the effect of the dilaton field on the thermal stability of the solutions.Comment: 16 pages, 15 figures, references added, to appear in Phys. Rev.

Reentrant phase transition of Born-Infeld-AdS black holes

We investigate thermodynamic phase structure and critical behaviour of Born-Infeld (BI) black holes in an anti-de Sitter (AdS) space, where the charge of the system can vary and the cosmological constant (pressure) is fixed. We find that the BI parameter crucially affects the temperature of the black hole when the horizon radius, $r_{+}$, is small. We observe that depending on the value of the nonlinear parameter, $\beta$, BI-AdS black hole may be identified as RN black hole for $Q\geq Q_{m}$, and Schwarzschild-like black hole for $Q<Q_{m}$, where $Q_{m}=1/\left(8\pi \beta \right)$ is the \textit{marginal} charge. We analytically calculate the critical point ($$) by solving the cubic equation and study the critical behaviour of the system. We also explore the behavior of Gibbs free energy for BI-AdS black hole. We find out that the phase behaviour of BI-AdS black hole depends on the charge $Q$. For $Q>Q_{c}$, the Gibbs free energy is single valued and the system is locally stable ($C_{Q}>0$), while for , it becomes multivalued and $C_{Q}<0$. In the range of , a first order phase transition occurs between small black hole (SBH) and large black hole (LBH). Interestingly enough, in the range of $Q_{t}\leq Q\leq Q_{z}$, a reentrant phase transition occurs between intermediate (large) black hole, SBH and LBH in Schwarzschild-type region. This means that in addition to the first order phase transition which separates SBH and LBH, a finite jump in Gibbs free energy leads to a \textit{% zeroth order} phase transition between SBH and intermediate black hole (LBH) where initiates from $Q=Q_{z}$ and terminates at $Q=Q_{t}$.Comment: 8 pages, 6 figures, two column