# Impact of Collisional Matter on the Late-Time Dynamics of f(R,T) Gravity

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## Abstract

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## 1. Introduction

## 2. $\mathit{f}(\mathit{R},\mathit{T})$ Gravity: Basic Formalism

- $f(R,T)={\alpha}_{1}{R}^{{\gamma}_{1}}{T}^{{\gamma}_{2}}+{\alpha}_{2}T$,
- $f(R,T)={\beta}_{1}{R}^{\mu}+{\beta}_{2}{R}^{\nu}+\frac{2{k}^{2}}{-1+3\omega}T+{\beta}_{3}{T}^{\frac{1}{2}-\frac{\sqrt{-1+\omega (3+\omega -3{\omega}^{2})}}{(1+\omega )\sqrt{-2+6\omega}}}+{\beta}_{4}{T}^{\frac{1}{2}+\frac{\sqrt{-1+\omega (3+\omega -3{\omega}^{2})}}{(1+\omega )\sqrt{-2+6\omega}}}\phantom{\rule{0.166667em}{0ex}}$.

## 3. Collisional Matter Model within $\mathit{f}(\mathit{R},\mathit{T})$ Theory and Late-Time Dynamics

#### 3.1. $f(R,T)$ Model I

- ${\alpha}_{1}{R}^{10}{T}^{-4/5}+{\alpha}_{2}T$ .

#### 3.2. $f(R,T)$ Model II

#### 3.3. Another Perspective of the Late-Time Cosmological Evolution of Dark Energy with Collisional Matter Fluid

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The evolution of deceleration parameter versus redshift z (

**left**) plot and the evolution of total effective equation of state (EoS) parameter versus the redshift z (

**right**) plot. The free parameter values were chosen to be ${\alpha}_{1}=20,{\alpha}_{2}=15,{\gamma}_{1}=10$, ${\gamma}_{2}=-0.7$, and ${\Omega}_{m}=0.3183$.

**Figure 2.**The evolution of $H\left(z\right)$ versus redshift z (

**left**) and the evolution of the dark energy EoS parameter versus the redshift z (

**right**). The free parameter values are ${\alpha}_{1}=20,{\alpha}_{2}=15,{\gamma}_{1}=10$, ${\gamma}_{2}=-0.7$, and ${\Omega}_{m}=0.3183$.

**Figure 3.**The evolution of deceleration parameter versus redshift z (

**left**) and the evolution of the total EoS parameter versus redshift z (

**right**). The free parameter values were chosen to be ${\beta}_{1}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}5,{\beta}_{2}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}10,{\beta}_{3}=15$, ${\beta}_{4}=20$, $\mu =25,\nu =30$, and $\Omega =0.3183$.

**Figure 4.**The evolution of $H\left(z\right)$ versus redshift z (

**left**) and the evolution of the dark energy EoS parameter versus the redshift z (

**right**). The free parameter values were chosen to be ${\beta}_{1}=5,$${\beta}_{2}=10,$${\beta}_{3}=15$, ${\beta}_{4}=20$, $\mu =25,\nu =30$, and $\Omega =0.3183$.

**Figure 5.**The evolution of ${y}_{H}\left(z\right)$ as a function of the redshift (

**left**), and the evolution of the dark energy EoS parameter as a function of the redshift (

**right**). The free parameter values were chosen to be, ${\alpha}_{1}=20,{\alpha}_{2}=15,{\gamma}_{1}=10$, ${\gamma}_{2}=-0.7$, and ${\Omega}_{m}=0.3183$.

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**MDPI and ACS Style**

Zubair, M.; Zeeshan, M.; Hasan, S.S.; Oikonomou, V.K.
Impact of Collisional Matter on the Late-Time Dynamics of *f*(*R*,*T*) Gravity. *Symmetry* **2018**, *10*, 463.
https://doi.org/10.3390/sym10100463

**AMA Style**

Zubair M, Zeeshan M, Hasan SS, Oikonomou VK.
Impact of Collisional Matter on the Late-Time Dynamics of *f*(*R*,*T*) Gravity. *Symmetry*. 2018; 10(10):463.
https://doi.org/10.3390/sym10100463

**Chicago/Turabian Style**

Zubair, M., Muhammad Zeeshan, Syed Sibet Hasan, and V. K. Oikonomou.
2018. "Impact of Collisional Matter on the Late-Time Dynamics of *f*(*R*,*T*) Gravity" *Symmetry* 10, no. 10: 463.
https://doi.org/10.3390/sym10100463