# Crossing of Phantom Divide Line in Model of Interacting Tsallis Holographic Dark Energy

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## Abstract

**:**

## 1. Introduction

## 2. Model Description

## 3. The Possibility of Phantom Line Crossing and Disappearing of Singularities Due to Interaction

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The effective state parameter for holographic dark energy (

**left, top**), the Hubble parameter (

**right, top**) and the derivative of the Hubble parameter (

**left, bottom**) and part of dark energy in total energy density (

**right, bottom**) as a function of time for $C=1$, $d=0$. Time is given in units of $1/{H}_{0}$, where ${H}_{0}$ is the value of the Hubble parameter at the present time.

**Figure 2.**Same as in Figure 1, but for $C=1$, ${d}^{2}=0.1$ (solid lines) and ${d}^{2}=0.2$ (dashed lines). For $\gamma =1.05$ and ${d}^{2}=0.1$, the value of ${w}_{de}$ intersects the phantom divide line ${w}_{0}=-1$ twice. Asymptotical values of ${w}_{de}$ for $\gamma =1$ and $\gamma =0.95$ are less than $-1$ but we have no singularities in the future and the universe expands according to the de Sitter law at $t\to \infty $.

**Figure 3.**Same as in Figure 1, but for $C=0.9$, $d=0$. For some $\gamma \ge 1$, big rip singularity in future takes place (green curve). For another $\gamma >1$, $H\to 0$. For $\gamma <1$, we have quasi-de Sitter expansion (${w}_{de}\to -1$) in future.

**Figure 4.**Same as in Figure 1, but for $C=0.9$, ${d}^{2}=0.1$ (solid lines) and ${d}^{2}=0.2$ (dashed lines). For $\gamma =1.05$ at ${d}^{2}=0.2$, there is no big rip singularity which takes place for ${d}^{2}=0.1$ and without interaction.

**Figure 5.**Evolution of the equation-of-state parameter and first derivative of the Hubble parameter for two values of ${C}^{2}$ in the case of $\gamma =1.05$ for various ${d}^{2}$. The value of the state parameter either “skips” into the negative region (slower than at ${d}^{2}=0$), or reaches the minimum ${w}_{min}<-1$ and starts growing (then there is no singularity in the future, the Hubble parameter decreases with time). These two cases are again separated by the value of ${d}_{crit}^{2}$ for specific C and $\gamma $.

**Figure 6.**Same as in Figure 1, but for $C=1.1$, $d=0$. For $\gamma <1$, the universe expands asymptotically according to the de Sitter law. $\gamma \ge 1$ corresponds to $H\to 0$.

**Figure 7.**Same as in Figure 1, but for $C=1.1$, ${d}^{2}=0.1$. Evolution of the universe is the same as without interaction but for quasi-de Sitter expansion ${w}_{de}\to {w}_{0}<-1$.

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**MDPI and ACS Style**

Astashenok, A.V.; Tepliakov, A.
Crossing of Phantom Divide Line in Model of Interacting Tsallis Holographic Dark Energy. *Universe* **2022**, *8*, 265.
https://doi.org/10.3390/universe8050265

**AMA Style**

Astashenok AV, Tepliakov A.
Crossing of Phantom Divide Line in Model of Interacting Tsallis Holographic Dark Energy. *Universe*. 2022; 8(5):265.
https://doi.org/10.3390/universe8050265

**Chicago/Turabian Style**

Astashenok, Artyom V., and Alexander Tepliakov.
2022. "Crossing of Phantom Divide Line in Model of Interacting Tsallis Holographic Dark Energy" *Universe* 8, no. 5: 265.
https://doi.org/10.3390/universe8050265