# Realization of Bounce in a Modified Gravity Framework and Information Theoretic Approach to the Bouncing Point

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Equation of State of Barotropic Fluid

## 3. Bounce Cosmology with Respect to E-Folding Number

## 4. Hubble Flow Dynamics

## 5. Inflation via Scalar Field

## 6. Fractional Density

## 7. MGCG in f(T) Gravity

## 8. Stability Analysis

## 9. Uncertainty Towards Bouncing Point

## 10. Discussion and Concluding Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Reconstructed density evolution in the modified generalized Chaplygin Gas scenario with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units for rainbow-dashed, red-solid curve, blue-solid curve and green-solid curve, respectively, with the bouncing point arising at $t=0$.

**Figure 2.**Reconstructed EoS parameter evolution in the modified generalized Chaplygin Gas scenario with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units for rainbow-dashed, red-solid curve, blue-solid curve and green-solid curve, respectively, with the bouncing point arising at $t=0$.

**Figure 3.**Reconstructed bulk viscous pressure $\mathrm{\Pi}$ evolution in the modified generalized Chaplygin Gas scenario with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units for black-solid, red-solid curve, blue-solid curve and green-solid curve, respectively.

**Figure 4.**Reconstructed bulk viscosity coefficient $\xi $ evolution in the modified generalized Chaplygin Gas scenario with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units for black-solid, red-solid curve, blue-solid curve and green-solid curve, respectively.

**Figure 5.**Reconstructed effective EoS parameter evolution in the modified generalized Chaplygin Gas scenario with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units for black-solid, red-solid curve, blue-solid curve and green-solid curve, respectively, with the bouncing point arising at $t=0$.

**Figure 6.**Evolution of expression of time derivative of e-folding Number with respect to cosmic time with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units for rainbow-dashed curve, rainbow-dotted curve, black-solid curve and rainbow-solid curve, respectively, the bouncing point at $t=0$.

**Figure 8.**Evolution of expression of ${\omega}_{eff}$ with respect to time derivative of e-folding number.

**Figure 14.**Evolution of fractional density with respect to cosmic time t with decreasing matter density shown by the solid-curve and increasing energy density by the dashed-curve with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units.

**Figure 15.**Reconstructed arbitrary torsion contributed function f evolution with respect to cosmic time t in the modified generalized Chaplygin Gas scenario with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units for orange-solid curve, red-solid curve, blue-solid curve and green-solid curve, respectively, with the bouncing point arising at $t=0$.

**Figure 16.**Reconstructed torsion contributed density evolution ${\rho}_{T}$ in the modified generalized Chaplygin Gas scenario with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.02$, $\u03f5=0.64$, $\gamma =0.68$ and $A=2.3$ varying $\sigma =(2.65,2.85,1.56,1.86)$ in units for rainbow-dashed curve, red-solid curve, blue-solid curve and green-solid curve, respectively, with the bouncing point arising at $t=0$.

**Figure 17.**Reconstructed torsion contributed EoS parameter evolution ${\omega}_{T}$ in the modified generalized Chaplygin Gas scenario with ${\rho}_{{m}_{0}}=0.32$, ${a}_{0}=0.2$, $\u03f5=0.43$, $\gamma =0.89$ and $A=0.96$ varying $\sigma =(2.34,3.85,4.56,4.86)$ in units for black-solid curve, red-solid curve, blue-solid curve and green-solid curve, respectively, with the bouncing point arising at $t=0$.

**Figure 19.**Evolution of square speed of sound ${V}_{s}^{2}>0$ for modified $f\left(T\right)$ gravity scenario.

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**MDPI and ACS Style**

Saha, S.; Chattopadhyay, S.
Realization of Bounce in a Modified Gravity Framework and Information Theoretic Approach to the Bouncing Point. *Universe* **2023**, *9*, 136.
https://doi.org/10.3390/universe9030136

**AMA Style**

Saha S, Chattopadhyay S.
Realization of Bounce in a Modified Gravity Framework and Information Theoretic Approach to the Bouncing Point. *Universe*. 2023; 9(3):136.
https://doi.org/10.3390/universe9030136

**Chicago/Turabian Style**

Saha, Sanghati, and Surajit Chattopadhyay.
2023. "Realization of Bounce in a Modified Gravity Framework and Information Theoretic Approach to the Bouncing Point" *Universe* 9, no. 3: 136.
https://doi.org/10.3390/universe9030136