# Quantum Cosmologies under Geometrical Unification of Gravity and Dark Energy

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## Abstract

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## 1. Introduction

## 2. Lagrangian for FRWq System

## 3. Quintessence and Fermat-Like Lagrangian

## 4. Quantization

#### 4.1. Quantization of the FRWq System as a Klein–Gordon Particle

#### 4.2. Quantization of the FRWq System à la Dirac-Pauli

#### 4.3. Quantization of the FRWq System à la Majorana

## 5. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Dirac Equation in Curved Spacetimes

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**MDPI and ACS Style**

Rubio, C.A.; Asenjo, F.A.; Hojman, S.A.
Quantum Cosmologies under Geometrical Unification of Gravity and Dark Energy. *Symmetry* **2019**, *11*, 860.
https://doi.org/10.3390/sym11070860

**AMA Style**

Rubio CA, Asenjo FA, Hojman SA.
Quantum Cosmologies under Geometrical Unification of Gravity and Dark Energy. *Symmetry*. 2019; 11(7):860.
https://doi.org/10.3390/sym11070860

**Chicago/Turabian Style**

Rubio, Carlos A., Felipe A. Asenjo, and Sergio A. Hojman.
2019. "Quantum Cosmologies under Geometrical Unification of Gravity and Dark Energy" *Symmetry* 11, no. 7: 860.
https://doi.org/10.3390/sym11070860