Horizon thermodynamics in holographic cosmological models with a power-law term

Abstract

Thermodynamics on the horizon of a flat universe at late times is studied in holographic cosmological models that assume an associated entropy on the horizon. In such models, a Λ(t) model similar to a time-varying Λ(t) cosmology is favored because of the consistency of energy flows across the horizon. Based on this consistency, a Λ(t) model with a power-law term proportional to H α is formulated to systematically examine the evolution of the Bekenstein-Hawking entropy. Here, H is the Hubble parameter and α is a free parameter whose value is a real number. The present model always satisfies the second law of thermodynamics on the horizon. In particular, the universe for α < 2 tends to approach thermodynamic equilibrium-like states. Consequently, when α < 2, the maximization of the entropy should be satisfied as well, at least in the last stage of the evolution of an expanding universe. A relaxation-like process before the last stage is also examined from a thermodynamics viewpoint. 95.30.Tg, 98.80.Es

Energy stored on a cosmological horizon and its thermodynamic fluctuations in holographic equipartition law

“…We consider a flat FRW universe and study the scale factor a(t) at time t. An expanding universe is assumed. In this section, a general formulation of the cosmological equations is reviewed, based on previous works [32,51,53]. Using the formulation, a holographic model that includes a power-law term is introduced, as a favored model close to ΛCDM models.…”

“…and w represents the equation of the state parameter for a generic component of matter, w = p(t) ρ(t)c 2 . Here, G, c, ρ(t), and p(t) are the gravitational constant, the speed of light, the mass density of cosmological fluids, and the pressure of cosmological fluids, respectively [32,51,53]. For a matter-dominated universe, a radiationdominated universe, and a Λ-dominated universe, w is 0, 1/3, and −1, respectively.…”

“…Alternatively, thermodynamic scenarios usually assume the 'holographic principle', that is, the information of the bulk is assumed to be stored on the horizon [33]. In those scenarios, the concept of black hole thermodynamics [34][35][36] is applied to the cosmological horizon [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. The holographic equipartition law [43] has also attracted attention and has been examined by many researchers [44][45][46][47][48][49][50][51][52][53].…”

“…In those scenarios, the concept of black hole thermodynamics [34][35][36] is applied to the cosmological horizon [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. The holographic equipartition law [43] has also attracted attention and has been examined by many researchers [44][45][46][47][48][49][50][51][52][53].…”

“…In addition, the thermodynamics of the Universe has been studied from various viewpoints . In particular, the maximization of entropy has been investigated recently [51][52][53][59][60][61][62][63][64][65], and these studies suggest that our Universe should approach a Λ-dominated universe, namely a de Sitter universe, at least in the last stage, as if our Universe behaves as an ordinary macroscopic system [59]. A de Sitter universe is considered to be in thermal equilibrium based on horizon thermodynamics.…”