Thermodynamic properties of modified gravity theories

Abstract

We review thermodynamic properties of modified gravity theories such as $F(R)$ gravity and $f(T)$ gravity, where $R$ is the scalar curvature and $T$ is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in $f(T)$ gravity. We show both equilibrium and non-equilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met when the temperature of the outside of the apparent horizon is equivalent to that of the inside of it.Comment: 27 pages, no figure, version accepted for publication in International Journal of Geometric Methods in Modern Physic

Equilibrium and stability of relativistic stars in extended theories of gravity

“…Notice that the second law of thermodynamics will differ in ETGs [42] but the above general relation remains valid in our treatment. This expression will be our starting point but before doing that we should investigate in detail the dependence of the variation δρ with respect to other quantities.…”

“…Moreover, we identify the quantity δM(r ) which appears in (42) as δM(r ) = ∞ 0 4πr 2 δ Q k dr . Applying such relations to Eq.…”

Dark energy and its manifestations

“…The universe possesses a non-zero cosmological constant, which is suggested by the observational data [8]. In the last few years the cosmological constant problems have been studied seriously, which promoted researchers to look in different ways in the names of dynamical dark energy models [10][11][12][13][14][15][16][17][18][19][20] , modified gravitational theories [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Consequently, the time varying Λ theory has attracted the attention of researchers in recent years to explore new findings.…”

A Thermodynamic Approach to Holographic Dark Energy

“…These issues do not enable concluding that the ΛCDM model represents the final paradigm to describe the universe dynamics (in particular, the measures of cosmological constant and matter magnitudes are extremely close to each other, i.e., Ω Λ /Ω ∼ 2.7, at our time [38,[47][48][49], whereas the predicted and observed cosmological constant values differ for about 123 orders of magnitude [50]). As a natural consequence, a wide amount of cosmological models has been introduced to extend the concordance model in 2 Advances in High Energy Physics order to get possible alternatives to dark energy derived from prime principles (see, e.g., [51][52][53][54][55][56][57][58][59] and references therein).…”