# Quantum Cosmology of the Big Rip: Within GR and in a Modified Theory of Gravity

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## Abstract

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## 1. Introduction

## 2. The Classical Big Rip Singularity

## 3. Quantum Cosmology of the Big Rip within the Holographic Ricci Dark Energy

## 4. Quantum Cosmology of the Big Rip Model within the Eddington-Inspired Born-Infeld Model

- If ${a}^{2}$ diverges slower than ${\mathrm{e}}^{2x}$ (i.e., $\delta \to 0$), the second term in the bracket in (15) is negligible compared with the first term. However, whether the first term dominates over the third term depends on the exact form of $\rho \left(a\right)$ and $\delta $. In either case, the potential reaches positive infinite values when both a and x go to infinity.
- If ${a}^{2}$ diverges faster than ${\mathrm{e}}^{2x}$ (i.e., $\delta \to \infty $), the potential can be approximated as$${V}_{1}\left(a,x\right)\approx \frac{24}{\kappa {\hslash}^{2}}{\left(\lambda +\kappa \rho \left(a\right)\right)}^{2}{a}^{6}$$
- If ${a}^{2}$ diverges comparably with ${\mathrm{e}}^{2x}$, the potential can also be approximated as in Equation (16), because the phantom energy density blows up when $a\to \infty $.

## 5. Conclusions and Further Discussions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

BR | Big Rip |

DE | dark energy |

DM | dark matter |

FLRW | Friedmann–Lemaître–Robertson–Walker |

HRDE | holographic Ricci dark energy |

EiBI | Eddington-Inspired-Born-Infeld |

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**Figure 1.**Schematic plot of the Big Rip (BR) singularity. In this plot, ${t}_{f}$ corresponds to the time of the occurrence of BR.

**Figure 2.**Plot that schematically shows the destruction of bounded structures when approaching the BR.

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Bouhmadi-López, M.; Albarran, I.; Chen, C.-Y.
Quantum Cosmology of the Big Rip: Within GR and in a Modified Theory of Gravity. *Universe* **2017**, *3*, 36.
https://doi.org/10.3390/universe3020036

**AMA Style**

Bouhmadi-López M, Albarran I, Chen C-Y.
Quantum Cosmology of the Big Rip: Within GR and in a Modified Theory of Gravity. *Universe*. 2017; 3(2):36.
https://doi.org/10.3390/universe3020036

**Chicago/Turabian Style**

Bouhmadi-López, Mariam, Imanol Albarran, and Che-Yu Chen.
2017. "Quantum Cosmology of the Big Rip: Within GR and in a Modified Theory of Gravity" *Universe* 3, no. 2: 36.
https://doi.org/10.3390/universe3020036