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A Sheykhi - One of the best experts on this subject based on the ideXlab platform.
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modified Friedmann equations from tsallis entropy
Physics Letters B, 2018Co-Authors: A SheykhiAbstract:Abstract 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 = γ A β , where A is the horizon area and β is the nonextensive parameter [1] . 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, d E = T h d S h + W d V , 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. Taking β = 2 / 5 , we find the age of the universe ranges as 13.12 Gyr t 0 16.32 Gyr, which is consistent with recent observations. Finally, using the Jeans's analysis, we comment, in brief, on the density perturbation in the context of Tsallis cosmology and found that the growth of energy differs compared to the standard cosmology.
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Friedmann equations from emergence of cosmic space
Physical Review D, 2013Co-Authors: A SheykhiAbstract:Padmanabhan [arXiv:1206.4916] argues that the cosmic acceleration can be understood from the perspective that spacetime dynamics is an emergence phenomena. By calculating the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space, he also arrives at the Friedmann equation in a flat universe. In this paper, by modification of his proposal, we are able to derive the Friedmann equation of the Friedmann-Robertson-Walker universe with any spatial curvature. We also extend the study to higher-dimensional spacetime and derive successfully the Friedmann equations not only in Einstein gravity but also in Gauss-Bonnet and more general Lovelock gravity with any spatial curvature. This is the first derivation of Friedmann equations in these gravity theories in a nonflat Friedmann-Robertson-Walker universe by using the novel idea proposed by Padmanabhan. Our study indicates that the approach presented here is powerful enough and further supports the viability of Padmanabhan's perspective of emergence gravity.
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entropic corrections to Friedmann equations
Physical Review D, 2010Co-Authors: A SheykhiAbstract: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 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 Friedmann 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.
Katherine Freese - One of the best experts on this subject based on the ideXlab platform.
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cardassian expansion dark energy density from modified Friedmann equations
New Astronomy Reviews, 2005Co-Authors: Katherine FreeseAbstract:Abstract The Cardassian universe is a proposed modification to the Friedmann equation in which the universe is flat, matter dominated, and accelerating. In the ordinary Friedmann equation, the right hand side is a linear function of the energy density, H 2 ∼ ρ . Here, instead, the right hand side of the Friedmann equation is a different function of the energy density, H 2 ∼ g ( ρ ). This function returns to ordinary Friedmann at early times, but drives acceleration of the universe at the current epoch. The only ingredients in this universe are matter and radiation: in particular, there is NO vacuum contribution. The new term required may arise, e.g., as a consequence of our observable universe living as a three-dimensional brane in a higher dimensional universe. A second possible interpretation of Cardassian expansion is developed, in which we treat the modified Friedman equations as due to a fluid, in which the energy density has new contributions with negative pressure (possibly due to dark matter with self-interactions). Predictions are shown for observational tests of generalized Cardassian models in future supernova surveys.
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cardassian expansion dark energy density from modified Friedmann equations
arXiv: Astrophysics, 2005Co-Authors: Katherine FreeseAbstract:The Cardassian universe is a proposed modification to the Friedmann equation in which the universe is flat, matter dominated, and accelerating. In the ordinary Friedmann equation, the right hand side is a linear function of the energy density, $H^2 \sim \rho$. Here, instead, the right hand side of the Friedmann equation is a different function of the energy density, $H^2 \sim g(\rho)$. This function returns to ordinary Friedmann at early times, but drives acceleration of the universe at the current epoch. The only ingredients in this universe are matter and radiation: in particular, there is NO vacuum contribution. The new term required may arise, e.g., as a consequence of our observable universe living as a 3-dimensional brane in a higher dimensional universe. A second possible interpretation of Cardassian expansion is developed, in which we treat the modified Friedman equations as due to a fluid, in which the energy density has new contributions with negative pressure (possibly due to dark matter with self-interactions). Predictions are shown for observational tests of generalized Cardassian models in future supernova surveys.
Ronggen Cai - One of the best experts on this subject based on the ideXlab platform.
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Friedmann equations from entropic force
Physical Review D, 2010Co-Authors: Ronggen Cai, Liming Cao, Nobuyoshi OhtaAbstract:In this paper, by use of the holographic principle together with the equipartition law of energy and the Unruh temperature, we derive the Friedmann equations of a Friedmann-Robertson-Walker universe.
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corrected entropy area relation and modified Friedmann equations
Journal of High Energy Physics, 2008Co-Authors: Ronggen Cai, Liming CaoAbstract:Applying Clausius relation, delta Q = TdS, to apparent horizon of a FRW universe with any spatial curvature, and assuming that the apparent horizon has temperature T = 1/(2 pi(r) over tildeA), and a quantum corrected entropy-area relation, S = A/4G + alpha lnA/4G, where (r) over tildeA and A are the apparent horizon radius and area, respectively, and alpha is a dimensionless constant, we derive modified Friedmann equations, which does not contain a bounce solution. On the other hand, loop quantum cosmology leads to a modified Friedmann equation H-2 = 8 pi G/3 rho(1-rho/rho(crit)). We obtain an entropy expression of apparent horizon of FRW universe described by the modified Friedmann equation. In the limit of large horizon area, resulting entropy expression gives the above corrected entropy-area relation, however, the prefactor alpha in the logarithmic term is positive, which seems not consistent with most of results in the literature that quantum geometry leads to a negative contribution to the area formula of black hole entropy.
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corrected entropy area relation and modified Friedmann equations
arXiv: High Energy Physics - Theory, 2008Co-Authors: Ronggen Cai, Liming CaoAbstract:Applying Clausius relation, $\delta Q=TdS$, to apparent horizon of a FRW universe with any spatial curvature, and assuming that the apparent horizon has temperature $T=1/(2\pi \tilde {r}_A)$, and a quantum corrected entropy-area relation, $S=A/4G +\alpha \ln A/4G$, where $\tilde {r}_A$ and $A$ are the apparent horizon radius and area, respectively, and $\alpha$ is a dimensionless constant, we derive modified Friedmann equations, which does not contain a bounce solution. On the other hand, loop quantum cosmology leads to a modified Friedmann equation $H^2 =\frac{8\pi G}{3}\rho (1-\rho/\rho_{\rm crit})$. We obtain an entropy expression of apparent horizon of FRW universe described by the modified Friedmann equation. In the limit of large horizon area, resulting entropy expression gives the above corrected entropy-area relation, however, the prefactor $\alpha$ in the logarithmic term is positive, which seems not consistent with most of results in the literature that quantum geometry leads to a negative contribution to the area formula of black hole entropy.
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first law of thermodynamics and Friedmann equations of Friedmann robertson walker universe
arXiv: High Energy Physics - Theory, 2005Co-Authors: Ronggen Cai, Sang Pyo KimAbstract:Applying the first law of thermodynamics to the apparent horizon of a Friedmann-Robertson-Walker universe and assuming the geometric entropy given by a quarter of the apparent horizon area, we derive the Friedmann equations describing the dynamics of the universe with any spatial curvature. Using entropy formulae for the static spherically symmetric black hole horizons in Gauss-Bonnet gravity and in more general Lovelock gravity, where the entropy is not proportional to the horizon area, we are also able to obtain the Friedmann equations in each gravity theory. We also discuss some physical implications of our results.
Ahmed Farag Ali - One of the best experts on this subject based on the ideXlab platform.
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minimal length Friedmann equations and maximum density
Journal of High Energy Physics, 2014Co-Authors: Adel Awad, Ahmed Farag AliAbstract:Inspired by Jacobson’s thermodynamic approach [4], Cai et al. [5, 6] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation [6] of Friedmann equations to accommodate a general entrop-yarea law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ, a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p = ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.
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planck scale corrections to Friedmann equation
arXiv: General Relativity and Quantum Cosmology, 2014Co-Authors: Adel M Awad, Ahmed Farag AliAbstract:Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde's proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to \emph{quantum gravity} such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde's proposal and two known models of GUPs, we obtain modifications to Newton's law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the $p=\omega \rho$ equation of state.
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planck scale corrections to Friedmann equation
Central European Journal of Physics, 2014Co-Authors: Adel M Awad, Ahmed Farag AliAbstract:Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.
Liming Cao - One of the best experts on this subject based on the ideXlab platform.
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Friedmann equations from entropic force
Physical Review D, 2010Co-Authors: Ronggen Cai, Liming Cao, Nobuyoshi OhtaAbstract:In this paper, by use of the holographic principle together with the equipartition law of energy and the Unruh temperature, we derive the Friedmann equations of a Friedmann-Robertson-Walker universe.
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corrected entropy area relation and modified Friedmann equations
Journal of High Energy Physics, 2008Co-Authors: Ronggen Cai, Liming CaoAbstract:Applying Clausius relation, delta Q = TdS, to apparent horizon of a FRW universe with any spatial curvature, and assuming that the apparent horizon has temperature T = 1/(2 pi(r) over tildeA), and a quantum corrected entropy-area relation, S = A/4G + alpha lnA/4G, where (r) over tildeA and A are the apparent horizon radius and area, respectively, and alpha is a dimensionless constant, we derive modified Friedmann equations, which does not contain a bounce solution. On the other hand, loop quantum cosmology leads to a modified Friedmann equation H-2 = 8 pi G/3 rho(1-rho/rho(crit)). We obtain an entropy expression of apparent horizon of FRW universe described by the modified Friedmann equation. In the limit of large horizon area, resulting entropy expression gives the above corrected entropy-area relation, however, the prefactor alpha in the logarithmic term is positive, which seems not consistent with most of results in the literature that quantum geometry leads to a negative contribution to the area formula of black hole entropy.
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corrected entropy area relation and modified Friedmann equations
arXiv: High Energy Physics - Theory, 2008Co-Authors: Ronggen Cai, Liming CaoAbstract:Applying Clausius relation, $\delta Q=TdS$, to apparent horizon of a FRW universe with any spatial curvature, and assuming that the apparent horizon has temperature $T=1/(2\pi \tilde {r}_A)$, and a quantum corrected entropy-area relation, $S=A/4G +\alpha \ln A/4G$, where $\tilde {r}_A$ and $A$ are the apparent horizon radius and area, respectively, and $\alpha$ is a dimensionless constant, we derive modified Friedmann equations, which does not contain a bounce solution. On the other hand, loop quantum cosmology leads to a modified Friedmann equation $H^2 =\frac{8\pi G}{3}\rho (1-\rho/\rho_{\rm crit})$. We obtain an entropy expression of apparent horizon of FRW universe described by the modified Friedmann equation. In the limit of large horizon area, resulting entropy expression gives the above corrected entropy-area relation, however, the prefactor $\alpha$ in the logarithmic term is positive, which seems not consistent with most of results in the literature that quantum geometry leads to a negative contribution to the area formula of black hole entropy.
