New entropy, thermodynamics of apparent horizon and cosmology

TL;DR

The paper introduces a novel horizon entropy $S_K = S_{BH}/(1+\gamma S_{BH})$ and develops its holographic dark-energy implications within flat FLRW cosmology. By applying the first law of apparent-horizon thermodynamics with $S_h=S_K$, it derives generalized Friedmann equations featuring a dynamical cosmological constant $\Lambda_{\rm eff}(H)$, and computes the dark-energy density $\rho_D$, pressure $p_D$, and the EoS $w_D$, showing a phantom-divide crossing. With suitable parameter choices, the model achieves current-era values $\Omega_{m0}\approx 0.315$ and $q_0\approx -0.535$, and it naturally recovers an inflationary de Sitter phase at early times. The framework is shown to be equivalent to a teleparallel $F(T)$ gravity theory, providing a coherent link between entropic cosmology and modified gravity as a viable alternative cosmology for the universe’s evolution.

Abstract

Here, we consider new nonadditive entropy of the apparent horizon $S_K=S_{BH}/(1+γS_{BH})$ with $S_{BH}$ being the Bekenstein--Hawking entropy. This is an alternative of the Rényi and Tsallis entropies, that allows us, by utilising the holographic principle, to develop entropic (holographic) dark energy. When $γ\rightarrow 0$ our entropy becomes the Bekenstein--Hawking entropy $S_{BH}$. The generalized Friedmann equations for Friedmann--Lemaître--Robertson--Walker (FLRW) spacetime for the barotropic matter fluid with $p=wρ$ were obtained. We compute the dark energy pressure $p_D$, density of energy $ρ_D$, the normalized density parameters $Ω_D$, $Ω_{m}$ and the deceleration parameter $q$ of the universe corresponding to our model. From the second modified Friedmann equation a dynamical cosmological constant was obtained. We show that at some model parameters $w$ and $γ$ we obtain $Ω_{m0}\approx 0.315$ and $q_0\approx -0.535$ which are in agreement with the Planck data. \cite{Aghanim}. It was shown that the model under consideration possesses the phantom divide for the EoS of dark energy. Thus, our model, by virtue of the holographic principle, can describe the universe inflation and the late time of the universe acceleration. It is shown that entropic cosmology with our entropy proposed is equivalent to cosmology based on the teleparallel gravity with the function $F(T)$ obtained. The holographic dark energy model with the generalised entropy of the apparent horizon can be of interest for new cosmology.

Figures (6)

• Figure 1: The function $\Lambda_{eff}$ versus $H$ at $b=\pi \gamma/G=1,2,3$. Figure 1 shows that $\Lambda_{eff}$ increases as $b$ increases. At $H\rightarrow 0$ ($R_h\rightarrow\infty$) we have $\Lambda_{eff}\rightarrow 3b$.
• Figure 2: The function $\Omega_m$ versus $x$. Figure 2 shows that $\Omega_m$ increases when $x$ increases. As $x\rightarrow \infty$ ($R_h\rightarrow 0$) we have $\Omega_m\rightarrow 1$.
• Figure 3: The function $w_D$ versus $x=H^2/b$ at $w=0, 1/3, 2/3$. At large $x$ the EoS parameter for dark energy $w_D$ approaches to $-1$, $\lim_{x\rightarrow\infty}w_D=-1$.
• Figure 4: Left panel: The function $\bar{H}$ versus $z$ at $\bar{b}=0.1$, $w=1/3, 0, -0.1$. According to Fig. 4, $\bar{H}$ increases as $z$ increases. At fixed $\bar{H}$, when EoS parameter for the matter $w$ increases the redshift $z$ decreases. Right panel: In accordance with figure if parameter $\bar{b}$ increases, at fixed $z$, the reduced Hubble parameter $\bar{H}$ also increases.
• Figure 5: The deceleration parameter $q$ versus $x$ at $w=0, 1/3, 2/3$. According to figure the deceleration parameter $q$ increases when the parameter $x$ increases. When the EoS parameter of the matter $w$ increases, at fixed $x$, the deceleration parameter $q$ also increases. There are two phases: universe acceleration $q<0$ and deceleration $q>0$.