Clausius relation and Friedmann equation in FRW universe model

Abstract

It has been shown that Friedmann equation of FRW universe can be derived from the first law of thermodynamics in Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, scalar-tensor gravity and f (R) gravity. Moreover, it was pointed out that the temperature of the apparent horizon can be obtained using the tunneling formalism for the corresponding observers defined by Kodama vector. In this article, we find that the energy flux through the apparent horizon can be determined by using the Kodama vector. This implies the fact that the Clausius relation and the first law of thermodynamics associated with the apparent horizon in FRW universe is relative to the Kodama observers. We illustrate the derivation of Friedmann equation, and also extend the study to the cases of Hořava-Lifshitz gravity and IR modified Hořava-Lifshitz gravity.

A Note on Friedmann Equation of FRW Universe in Deformed Hořava—Lifshitz Gravity from Entropic Force

“…As we know, when the parameter ω of the HL gravity approaches infinite, the Einstein gravity will be recovered. Setting ω → ∞, we can see that the first term in (21) vanishes and the standard Friedmann equation will be obtained, which is exactly consistent with the result in [30].…”

“…Much work in this field has been made [62][63][64][65][66][67]. Assuming that the entropy/area relation in Hořava-Lifshitz gravity is S = A/4, the standard Friedmann equation was obtained in [30] from the clausius relation.…”

Apparent Horizon and Gravitational Thermodynamics of Universe in the Eddington-Born-Infeld Theory

“…The results of Ref. [5] was soon generalized to other theories of gravity, such as the scalar-tensor gravity [6], f (R) gravity [7], braneworld scenarios [8][9][10], generic f (R, φ, ∇ µ φ∇ µ φ) gravity [11], and Horava-Lifshitz gravity [12,13], to construct the effective total energy differentials by the corresponding modified Friedmann equations.…”

Oscillating universe in Hořava-Lifshitz gravity

“…In particular, we find nonsingular behavior in a high curvature region, which may lead to avoidance of a big bang initial singularity [4]. Many studies on the dynamics of the FLRW universe in HL gravity have come out within the last few years [2][3][4][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

“…As for matter components, a perfect fluid with the equation of state P ¼ w and a scalar field have been discussed. As a result, we can classify the analyzed models into four types: (1) the model with the detailed balance condition and with a perfect fluid [42][43][44][45][46][47][48][49][50][51], (2) the model with the detailed balance condition and with a scalar field [2,4,58], (3) the model without the detailed balance condition and with a perfect fluid [52][53][54][55][56][57]60], and (4) the model without the detailed balance condition and with a scalar field [3,59].…”