# Is the Axionic Dark Matter an Equilibrium System?

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## Abstract

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## 1. Introduction

## 2. Formalism of Axionic Extension of the Einstein-Aether Theory

#### 2.1. The Action Functional

#### 2.2. Modifications of the Pseudoscalar Field Potential

#### 2.2.1. Higgs Type Potential

#### 2.2.2. Periodic Potential of the Axion Field

#### 2.2.3. Equilibrium State of the Axion Field

#### 2.3. Master Equations for the Pseudoscalar, Vector, and Gravitational Fields

#### 2.3.1. Master Equation for the Axion Field

#### 2.3.2. Equations for the Unit Dynamic Vector Field

#### 2.3.3. Equations for the Gravitational Field

## 3. Application to the Friedmann-Type Cosmological Model

#### 3.1. Reduced Master Equations

#### 3.1.1. Reduced Equations for the Unit Vector Field

#### 3.1.2. Reduced Equation for the Pseudoscalar (Axion) Field

#### 3.1.3. The Key Equation for the Gravitational Field

#### 3.2. Equilibrium State with Vanishing Axion Field

#### 3.2.1. The Solution with the Periodic Potential

#### 3.2.2. The Solution with the Higgs Type Potential

#### 3.3. Equilibrium State with Non-Vanishing Axion Field

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Balakin, A.B.; Shakirzyanov, A.F.
Is the Axionic Dark Matter an Equilibrium System? *Universe* **2020**, *6*, 192.
https://doi.org/10.3390/universe6110192

**AMA Style**

Balakin AB, Shakirzyanov AF.
Is the Axionic Dark Matter an Equilibrium System? *Universe*. 2020; 6(11):192.
https://doi.org/10.3390/universe6110192

**Chicago/Turabian Style**

Balakin, Alexander B., and Amir F. Shakirzyanov.
2020. "Is the Axionic Dark Matter an Equilibrium System?" *Universe* 6, no. 11: 192.
https://doi.org/10.3390/universe6110192