# Bubble Nucleation from a de Sitter–Planck Background with Quantum Boltzmann Statistics

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## Abstract

**:**

## 1. Introduction

## 2. The Multiverse in the de Sitter–Planck Background with Quantum Boltzmann Statistics

- (1)
- The particle is initially massless (namely, it corresponds to the vacuum state);
- (2)
- Its localization in an interaction event requires an amount of energy equal to the ratio of $\hslash $ and an opportune duration corresponding to the transition hypersurface ${\mathsf{\Sigma}}_{\frac{1}{\sqrt{\mathsf{\Lambda}}}}$ generating the appearance of time; thus, the fluctuations of the quantum vacuum are associated with the appearance of a particle take place;
- (3)
- The particle self-interacts for a duration of $\hslash /{M}_{dim}{c}^{2}$, and therefore on a scale of lengths equal to $\hslash /{M}_{dim}c$. The total mass of the real particle is therefore the sum of the “bare” mass associated with the bubbles of the de Sitter–Planck vacuum and the $\epsilon /{c}^{2}$ mass derived from this self-interaction.

## 3. Bubbles Geometry and the Generalized Uncertainty Relations

## 4. From the Generalized Uncertainty Relations to Sub-Planckian Black Holes

## 5. Thermodynamics of a Quantum Black Hole

## 6. Casimir Energy and Cosmological Wormholes

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Fiscaletti, D.; Licata, I.; Tamburini, F.
Bubble Nucleation from a de Sitter–Planck Background with Quantum Boltzmann Statistics. *Symmetry* **2022**, *14*, 2297.
https://doi.org/10.3390/sym14112297

**AMA Style**

Fiscaletti D, Licata I, Tamburini F.
Bubble Nucleation from a de Sitter–Planck Background with Quantum Boltzmann Statistics. *Symmetry*. 2022; 14(11):2297.
https://doi.org/10.3390/sym14112297

**Chicago/Turabian Style**

Fiscaletti, Davide, Ignazio Licata, and Fabrizio Tamburini.
2022. "Bubble Nucleation from a de Sitter–Planck Background with Quantum Boltzmann Statistics" *Symmetry* 14, no. 11: 2297.
https://doi.org/10.3390/sym14112297