# Nonsingular Phantom Cosmology in Five-Dimensional f(R, T) Gravity

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modified Einstein Field Equations

## 3. Solutions to the Field Equations

#### 3.1. $f(R,T)=\mu R+\mu T$

#### 3.2. $f(R,T)=R+\mu {R}^{2}+\mu T$

#### 3.3. $f(R,T)=R\mu +RT{\mu}^{2}$

## 4. Some Physical and Geometrical Properties

#### 4.1. Status of the Model

#### 4.2. Stability of the Model

#### 4.3. EOS Parameter $\left(w\right)$

## 5. Discussion and Conclusions

- (1)
- We notice that the model is free from the initial singularity and, hence, physically viable. This feature is obvious, as for $\tau =0$, we obtain $V=1$, and for $\tau \to \infty $, one can obtain $V\to \infty $.
- (2)
- The cosmic distribution has a finite fluid pressure and matter density at $\tau =0$. The physical quantities decrease as $\tau $ increases and tend to zero when $\tau \to \infty $. Thus, our presented model leads to a vacuum cosmological solution at infinite time.
- (3)
- As $\frac{{\sigma}^{2}}{{\theta}^{2}}\ne 0$, so the model is anisotropic throughout the evolution. Again, $\tau \to \infty $ exhibits the expanding universe. However, $q=3$ dictates that the universe is decelerating.
- (4)
- The stability of the model is obtained by considering the ratio $\frac{dp}{d\rho}$, which is positive for $\mu >-4\pi $, to yield a stable model.
- (5)
- The EOS parameter is governed by the parameter $\mu $, and its value can be found as $\mu <-3.2\pi $. This is related to $w<-1$, which behaves like a phantom-energy-inspired cosmology. This type of phantom cosmology allows us to account for the dynamics and matter content of the universe, tracing back the evolution to the inflationary epoch [74]. In this connection, we would also like to point out that while the dependence of $\mu $ is explicit across all cases, this is not overall true, as this situation is solely visible in the results from Case 3.1. One can note that Case 3.3 shows a clear time dependence (and therefore, very dependent on the magnitude of ${c}_{2}$).
- (6)
- The anisotropic/isotropic behavior of the models for different choices of the parameters are given in Table 1 in connection with Case 3.2.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Variation of the pressure and density w.r.t. time (Case 3.1). Here, we considered the following parametric values: ${k}_{1}=0.13$, ${k}_{3}=0.1$, and $m=0.5$, which will also be followed in all other plots.

For Case 3.2 | ${\mathit{k}}_{1}={\mathit{k}}_{3}$, $\mathit{m}=1$ | ${\mathit{k}}_{1}={\mathit{k}}_{3}$, $\mathit{m}=-1$ | ${\mathit{k}}_{1}=-{\mathit{k}}_{3}$, $\mathit{m}=1$ | ${\mathit{k}}_{1}=-{\mathit{k}}_{3}$, $\mathit{m}=-1$ |
---|---|---|---|---|

V | expanding | expanding | decreasing | constant |

$\theta $ | decreasing | decreasing | negative | 0 |

q | 3 | 3 | 3 | undefined |

z | decreasing | decreasing | increasing | 0 |

$\frac{{\sigma}^{2}}{{\theta}^{2}}$ | 0 | $\frac{3}{8}$ | $\frac{3}{8}$ | undefined |

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**MDPI and ACS Style**

Sahoo, R.R.; Mahanta, K.L.; Ray, S.
Nonsingular Phantom Cosmology in Five-Dimensional *f*(*R*, *T*) Gravity. *Universe* **2022**, *8*, 573.
https://doi.org/10.3390/universe8110573

**AMA Style**

Sahoo RR, Mahanta KL, Ray S.
Nonsingular Phantom Cosmology in Five-Dimensional *f*(*R*, *T*) Gravity. *Universe*. 2022; 8(11):573.
https://doi.org/10.3390/universe8110573

**Chicago/Turabian Style**

Sahoo, Rakesh Ranjan, Kamal Lochan Mahanta, and Saibal Ray.
2022. "Nonsingular Phantom Cosmology in Five-Dimensional *f*(*R*, *T*) Gravity" *Universe* 8, no. 11: 573.
https://doi.org/10.3390/universe8110573