Interacting entropy-corrected holographic dark energy with apparent horizon as an infrared cutoff

TL;DR

This work studies entropy-corrected holographic dark energy models—logarithmic LECHDE and power-law PLECHDE—with the apparent horizon serving as the infrared cutoff in a non-flat FRW universe. It analyzes both interacting and non-interacting dark sectors, derives evolution equations for the density ratio $u$, the equation of state $w_D$, and the deceleration parameter $q$, and develops a thermodynamic interpretation of the DE–DM interaction via horizon thermodynamics. The results show that cosmic coincidence can be alleviated for suitable parameter values, and that phantom-divide crossing along with late-time acceleration can occur when interaction is present; a thermodynamic link between the interaction term and thermal fluctuations is established, with consistency checks against the ordinary HDE limit. Collectively, the paper provides a unified framework combining entropy corrections, horizon thermodynamics, and interaction effects to explain current cosmic acceleration in a curved spacetime.

Abstract

In this work we consider the entropy-corrected version of interacting holographic dark energy (HDE), in the non-flat universe enclosed by apparent horizon. Two corrections of entropy so-called logarithmic 'LEC' and power-law 'PLEC' in HDE model with apparent horizon as an IR-cutoff are studied. The ratio of dark matter to dark energy densities $u$, equation of state parameter $w_D$ and deceleration parameter $q$ are obtained. We show that the cosmic coincidence is satisfied for both interacting models. By studying the effect of interaction in EoS parameter, we see that the phantom divide may be crossed and also find that the interacting models can drive an acceleration expansion at the present and future, while in non-interacting case, this expansion can happen only at the early time. The graphs of deceleration parameter for interacting models, show that the present acceleration expansion is preceded by a sufficiently long period deceleration at past. Moreover, the thermodynamical interpretation of interaction between LECHDE and dark matter is described. We obtain a relation between the interaction term of dark components and thermal fluctuation in a non-flat universe, bounded by the apparent horizon. In limiting case, for ordinary HDE, the relation of interaction term versus thermal fluctuation is also calculated.

Figures (6)

• Figure 1: The evolution of $u$ in versus $\widetilde{r}_{A}$ in LECHDE model. The asymptotic value is $u=0.56$.
• Figure 2: The evolution of EoS parameter, $w_{D}$, versus of $\widetilde{r}_{A}$ in LECHDE model, a:$0.22>\widetilde{r}_{A}>0.0$. b:$\widetilde{r}_{A}>0.23$.
• Figure 3: The evolution of $q$ in versus $x=\ln{(a)}$ in LECHDE model for ($n=0.8,~\gamma=0.1,~\beta=0.2,~b^2=.1,~\Gamma=0.04$).
• Figure 4: The evolution of $u$ in versus of $\widetilde{r}_{A}$ in PLECHDE model.
• Figure 5: The evolution of EoS parameter, $w_{D}$, in versus of $\widetilde{r}_{A}$ in PLECHDE model. a:$0.08>\widetilde{r}_{A}>0.0$ and $\delta=0.2$. b:$\widetilde{r}_{A}>0.09$ and $\delta=0.2$. "Q" the Quintessence barrier ($w_{D}=-1/3$).