A note on the relations between thermodynamics, energy definitions and Friedmann equations

Abstract

In what follows, we investigate the relation between the Friedmann and thermodynamic pressure equations, through solving the Friedmann and thermodynamic pressure equations simultaneously. Our investigation shows that a perfect fluid, as a suitable solution for the Friedmann equations leading to the standard modeling of the universe expansion history, cannot simultaneously satisfy the thermodynamic pressure equation and those of Friedmann. Moreover, we consider various energy definitions, such as the Komar mass, and solve the Friedmann and thermodynamic pressure equations simultaneously to get some models for dark energy. The cosmological consequences of obtained solutions are also addressed. Our results indicate that some of obtained solutions may unify the dominated fluid in both the primary inflationary and current accelerating eras into one model. In addition, by taking into account a cosmic fluid of a known equation of state, and combining it with the Friedmann and thermodynamic pressure equations, we obtain the corresponding energy of these cosmic fluids and face their limitations. Finally, we point out the cosmological features of this cosmic fluid and also study its observational constraints.

Energy Definition and Dark Energy: A Thermodynamic Analysis

“…In summary, i) The energy definition and the form of energy-momentum conservation law play crucial roles in getting the Friedmann equations in various theories [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. ii) We also showed the form of energy-momentum conservation law depends on the energy definition, and if one uses the Komar mass, then KCL is obtained instead of OCL.…”

“…3H 2 + 2Ḣ = 8π ∂E ∂V , ρ + 3H(ρ + p) = 0, instead of Eqs. (2), in order to study the relations between energy definitions, thermodynamics laws and the cosmic evolution, which led to a model for the cosmic fluid consistent with observations [19]. The Einstein field equations also admit another mass definition, namely the Komar mass [47,50,51]…”

“…Indeed, the validity of OCL is crucial, and its relaxation leads to modification of the Friedmann equations [14][15][16]18]. These results propose that the cosmos is so close to its thermodynamic equilibrium state [19][20][21][22][23][24][25][26][27][28], motivating us to be more confident on thermodynamical quantities, such as pressure, to study the cosmos [19]. For a FRW background filled by a fluid whose energy density ρ is at most a function of time, we may reach…”

“…Thus, if we have p 0 = w 0 c and c = Λ > 0, where Λ and w 0 denote the current values of the energy density and the equation of state (EoS) of dark energy, respectively, then the obtained fluid may theoretically generate the current accelerating universe whenever w 0 ≤ −2 3 . Now, we can write p(a) = w 0 Λa −3 , ρ(a) = Λa −3 [1 − 3w 0 ln(a)] (19).…”

Thermodynamic Analysis of Gravitational Field Equations in Lyra Manifold

“…The Riemannian geometry is the backbone of most of these theories, and it has been shown that the system horizon (as the boundary of system) has entropy, and indeed, there is a deep connection between the thermodynamics laws and the gravitational field equations . This mutual relation between gravity and thermodynamics may help us in providing a description for the primary inflationary era as well as the current accelerating phase of universe [34]. In addition, due to such relation, geometry and the universe material content may approach a thermodynamic equilibrium [35].…”