# Cosmological Particle Production in Quantum Gravity

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## Abstract

**:**

## 1. Introduction

## 2. Quantum Fields on a Quantum FLRW Spacetime

#### 2.1. Quantum Field on a Cosmological Classical Spacetime

#### 2.2. Quantization of the Background

#### 2.3. Emergence of Anisotropic Dressed Spacetimes

## 3. QFT on the Dressed Spacetime

#### 3.1. Field Equation on the Dressed Anisotropic Background

- (i)
- For massive field with undressed mass, $\tilde{m}=m\ne 0$, the relation for $\tilde{c}\left(\tilde{\eta}\right)$ has the form$$\tilde{c}\left(\tilde{\eta}\right)=\frac{{\u2329{\widehat{H}}_{o}^{-\frac{1}{2}}{\widehat{a}}^{6}{\widehat{H}}_{o}^{-\frac{1}{2}}\u232a}^{\frac{1}{3}}}{{\langle {\widehat{H}}_{o}^{-1}\rangle}^{\frac{1}{3}}}.$$
- (ii)
- For a massive field with the dressed mass, $\tilde{m}\ne m$, or a massless field, $\tilde{c}\left(\tilde{\eta}\right)$ has the solutions of the form$$\tilde{c}\left(\tilde{\eta}\right)={\xi}^{2}\frac{{\u2329{\widehat{H}}_{o}^{-\frac{1}{2}}{\widehat{a}}^{4}{\widehat{H}}_{o}^{-\frac{1}{2}}\u232a}^{\frac{1}{2}}}{{\langle {\widehat{H}}_{o}^{-1}\rangle}^{\frac{1}{2}}}={\xi}^{2}{\tilde{a}}^{2}\left(\tilde{\eta}\right),$$

#### 3.2. The Adiabatic Condition and the Vacuum State

## 4. Gravitational Particle Production

## 5. Conclusions and Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

## Notes

1. | We consider an elementary cell $\mathcal{V}$ by fixing its edge to lie along the coordinates $({\ell}_{1},{\ell}_{2},{\ell}_{3})$. We then denote the volume of $\mathcal{V}$ by $\stackrel{\u02da}{V}={\ell}_{1}{\ell}_{2}{\ell}_{3}\equiv {\ell}^{3}$, and restrict all integrations in the Fourier integral to this volume. |

2. | Note that our aim at the moment is just to avoid the UV divergence terms when regularizing the energy-momentum of the field. However, to have a more complete mode solution, in particular, when exploring the issues of the particle productions or backreaction effects, as we will see later, higher order terms in ${W}_{k}\left(\tilde{\eta}\right)$ should be taken into account. |

3. | They satisfy the normalization condition (Equation (49)) for the mode functions. |

4. | It should be noticed that the standard WKB ansatz may yield a divergent asymptotic series in the adiabatic parameter. Thus, when investigating the particle production in a time-dependent background, an optimal number of terms in that series should be chosen so that the resulting truncated WKB series becomes exponentially small. Such precision would still be insufficient to describe particle production from vacuum. Therefore, an adequately precise approximation should be employed by improving the WKB ansatz [34]. |

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Tavakoli, Y.
Cosmological Particle Production in Quantum Gravity. *Universe* **2021**, *7*, 258.
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Tavakoli Y.
Cosmological Particle Production in Quantum Gravity. *Universe*. 2021; 7(8):258.
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2021. "Cosmological Particle Production in Quantum Gravity" *Universe* 7, no. 8: 258.
https://doi.org/10.3390/universe7080258