# Scalar Field Models of Barrow Holographic Dark Energy in f(R,T) Gravity

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## Abstract

**:**

## 1. Introduction

## 2. Barrow Holographic Dark Energy

## 3. Assessment of Gravitational Field Equations of $f(R,T)$ Theory

## 4. The Cosmological Model

## 5. Correspondence with Scalar Field Models

#### 5.1. Quintessence Model for Barrow Hologaphic Dark Energy

#### 5.2. k-Essence Model for Barrow Holographic Dark Energy

#### 5.3. Dilation Model for Barrow Holographic Dark Energy

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Depicting the nature between the redshift(z) and the Barrow holographic quintessence scalar field $\left({\varphi}_{q}\right)$, (

**a**) $\left({\varphi}_{q}\right)$ is positive and (

**b**) $\left({\varphi}_{q}\right)$ is negative; here, $C=3$ and $\lambda =-5\pi $.

**Figure 2.**The plot of the Barrow holographic quintessence potential versus redshift (z); here, $C=3$ and $\lambda =-5\pi $.

**Figure 3.**The behaviour of the Barrow holographic quintessence potential (${V}_{q}\left(\varphi \right)$) versus the scalar field ($\varphi $): (

**a**) $\left({\varphi}_{q}\right)$ is positive and (

**b**) $\left({\varphi}_{q}\right)$ is negative; here, $C=3$ and $\lambda =-5\pi $.

**Figure 4.**Depicting the nature between the redshift (z) and the Barrow holographic k essence: (

**a**) $\left(\varphi \right)$ is positive and (

**b**) $\left(\varphi \right)$ is negative; here, $C=3$ and $\lambda =-5\pi $.

**Figure 5.**The behaviour of the Barrow holographic k-essence potential against redshifts (z); here, $C=3$ and $\lambda =-5\pi $.

**Figure 6.**The plot of the Barrow holographic k-essence potential ($f\left(\varphi \right)$) against the scalar field ($\varphi $): (

**a**) $\left(\varphi \right)$ is positive and (

**b**) $\left(\varphi \right)$ is negative. Here, $C=3$ and $\lambda =-5\pi $.

**Figure 7.**Depicting the nature between the redshift (z) and the scalar field of the Barrow holographic dilation $\left({\varphi}_{d}\right)$, (

**a**) $\left({\varphi}_{d}\right)$ is positive and (

**b**) $\left({\varphi}_{d}\right)$ is negative; here, $C=3$ and $\lambda =-5\pi $.

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Sharma, U.K.; Kumar, M.; Varshney, G.
Scalar Field Models of Barrow Holographic Dark Energy in *f*(*R*,*T*) Gravity. *Universe* **2022**, *8*, 642.
https://doi.org/10.3390/universe8120642

**AMA Style**

Sharma UK, Kumar M, Varshney G.
Scalar Field Models of Barrow Holographic Dark Energy in *f*(*R*,*T*) Gravity. *Universe*. 2022; 8(12):642.
https://doi.org/10.3390/universe8120642

**Chicago/Turabian Style**

Sharma, Umesh Kumar, Mukesh Kumar, and Gunjan Varshney.
2022. "Scalar Field Models of Barrow Holographic Dark Energy in *f*(*R*,*T*) Gravity" *Universe* 8, no. 12: 642.
https://doi.org/10.3390/universe8120642