# Thermodynamics of Barrow Holographic Dark Energy with Specific Cut-Off

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## Abstract

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**102**, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking that triggers a phase transition from early inflation to late-time acceleration. In the present study, we incorporated viscosity in the Barrow HDE. A reconstruction scheme is presented for the parameters associated with Barrow holographic dark energy under the purview of viscous cosmology. The equation of state (EoS) parameter is reconstructed in this scenario and quintessence behaviour is observed. Considering Barrow HDE as a specific case of Nojiri–Odintsov (NO) HDE, we have observed quintom behaviour of the EoS parameter and for some values of n the EoS has been observed to be very close to $-1$ for the current universe. The generalised second law of thermodynamics has come out to be valid in all the scenarios under consideration. Physical viability of considering Barrow HDE as a specific case of NO HDE is demonstrated in this study. Finally, it has been observed that the model under consideration is very close to $\Lambda $CDM and cannot go beyond it.

## 1. Introduction

## 2. Viscous Barrow Holographic Dark Energy

## 3. Generalised Second Law of Thermodynamics of Viscous Barrow HDE

## 4. Barrow HDE as a Specific NO HDE

#### 4.1. Generalised Second Law of Thermodynamics for Barrow HDE with NO Cut-Off

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Evolution of effective equation of state (EoS) (Equation (19)) of viscous Barrow Holographic Dark Energy against redshift z. The red, green and blue lines correspond to $n=0.7,0.8,0.9$, respectively.

**Figure 2.**Evolution of density of Barrow holographic dark energy (HDE) (Equation (16)) against $\Delta $. The red, green and blue line corresponds to $z=-0.1,0,0.1$, respectively.

**Figure 4.**Plot of ${\dot{S}}_{total}$ of viscous Barrow HDE against the cosmic time t and $\Delta $.

**Figure 5.**Evolution of the EoS parameter for Barrow HDE generalised through the Nojiri–Odintsov (NO) cut-off, i.e., ${w}_{BarrowHDE}$ against the redshift z and against n.

**Figure 6.**Plot of ${\dot{S}}_{total,BarrowHDE}$ of Barrow HDE with NO cut-off against the cosmic time t. The red, green and blue lines correspond to n=$0.9$, $0.8$ and $0.7$, respectively.

**Figure 7.**The statefinder trajectory for the reconstructed Barrow HDE. The $\Lambda $CDM fixed point is found to be attainable by the model.

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**MDPI and ACS Style**

Chakraborty, G.; Chattopadhyay, S.; Güdekli, E.; Radinschi, I.
Thermodynamics of Barrow Holographic Dark Energy with Specific Cut-Off. *Symmetry* **2021**, *13*, 562.
https://doi.org/10.3390/sym13040562

**AMA Style**

Chakraborty G, Chattopadhyay S, Güdekli E, Radinschi I.
Thermodynamics of Barrow Holographic Dark Energy with Specific Cut-Off. *Symmetry*. 2021; 13(4):562.
https://doi.org/10.3390/sym13040562

**Chicago/Turabian Style**

Chakraborty, Gargee, Surajit Chattopadhyay, Ertan Güdekli, and Irina Radinschi.
2021. "Thermodynamics of Barrow Holographic Dark Energy with Specific Cut-Off" *Symmetry* 13, no. 4: 562.
https://doi.org/10.3390/sym13040562