Thermodynamics in $f(R,R_{αβ}R^{αβ},ϕ)$ theory of gravity

Abstract

First and second laws of black hole thermodynamics are examined at the apparent horizon of FRW spacetime in f (R, R αβ R αβ , φ) gravity, where R, R αβ R αβ and φ are the Ricci scalar, Ricci invariant and the scalar field respectively. In this modified theory, Friedmann equations are formulated for any spatial curvature. These equations can be presented into the form of first law of thermodynamics for T h d Ŝh + T h d i Ŝh + W dV = dE, where d i Ŝh is an extra entropy term because of the non-equilibrium presentation of the equations and T h d Ŝh +W dV = dE for the equilibrium presentation. The generalized second law of thermodynamics (GSLT) is expressed in an inclusive form where these results can be represented in GR f (R) and f (R, φ) gravities. Finally to check the validity of GSLT, we take some particular models and produce constraints of the parameters.

Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

“…Moreover, upon variation of the action (151), with respect to the metric ĝµν , and also with respect to the scalar field φ, the gravitational equations are equal to,…”

“…Also, upon variation of the action (151), with respect to the mimetic scalar degree of freedom φ, we obtain,…”

“…where F ′ (R) = dF (R) dR . By using an auxiliary scalar field φ, the F (R) gravity action (151) can be written as follows,…”

“…Finally for some different scenarios see [100][101][102][103][141][142][143][144][145][146][147]. Also modified gravity usually brings along various exotic features, for example the equivalence principle can be different in comparison to the ordinary Einstein gravity [148], or the energy conditions may differ [149] and in addition the thermodynamic interpretation is different [150], see also [151]. But inevitably modified gravity has eventually to confront the successes of the Einstein-Hilbert gravity, so stringent rules are imposed from solar system tests.…”