# Interaction of the Cosmic Dark Fluid with Dynamic Aether: Parametric Mechanism of Axion Generation in the Early Universe

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation of the Work

#### 1.1.1. Inflation vs. Super-Inflation

#### 1.1.2. Dynamic Aether as a Guiding Element of the Cosmic Evolution

#### 1.1.3. Interaction of the Dynamic Aether with Dark Fluid

#### 1.1.4. The Role of Axionic Dark Matter in Our Approach

#### 1.2. The Structure of the Work

## 2. The Formalism

#### 2.1. The Total Action Functional

#### 2.2. Auxiliary Elements of Analysis

#### 2.3. Master Equations of the Model

#### 2.3.1. Master Equations for the Unit Vector Field

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

#### 2.3.3. Master Equations for the Gravitational Field

#### 2.3.4. Bianchi Identity and Conservation Law

## 3. Application to the Spatially Isotropic Homogeneous Cosmological Model

#### 3.1. The Spacetime Platform and Reduced Master Equations

#### 3.1.1. Solution to the Equations of the Vector Field

#### 3.1.2. Reduced Equation for the Axion Field

#### 3.1.3. Key Equations for the Gravity Field

#### 3.2. Super-Inflationary Scenario of Early Universe Evolution

#### 3.2.1. Epoch of the Dark Fluid Domination

#### 3.2.2. Exact Explicit Solutions in the Model of Super-Inflation

#### 3.2.3. On the Stability of the Axion Field Configuration

#### 3.3. Periodic Episode of the Early Universe Evolution

#### 3.3.1. Modifications of the Model

#### 3.3.2. Exact Solutions in the Periodic Model

#### 3.3.3. Parametric Generation of the Axion Field

#### 3.4. Remark about the Post-Inflationary Stage of the Universe Evolution

#### 3.4.1. Frozen Axion Field with Non-Vanishing Effective Cosmological Constant

#### 3.4.2. Frozen Axion Field with Vanishing Effective Cosmological Constant

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Illustration of the behavior of the super-exponential function $\frac{a\left(t\right)}{a\left({t}_{0}\right)}=exp\left\{\frac{1}{\rho}sinh\rho {H}_{0}(t-{t}_{0})\right\}$ for four values of the dimensionless parameter $\rho =\frac{1}{{H}_{0}}\gamma \sqrt{3{\kappa}_{*}W\left({t}_{0}\right)}$. For illustration, we put $H\left({t}_{0}\right)={H}_{0}=1$. The curve with $\rho =0$ corresponds to the de Sitter type regime (inflation).

**Figure 3.**Illustration of the behavior of the scale factor during the periodic episode of the Universe evolution. The interval of time $t<{t}_{0}$ relates to the epoch of the quantum regime of the expansion; near the moment $t={t}_{0}$, the ratio $\frac{a\left({t}_{0}\right)}{a\left(0\right)}$ reached the value of the order ${10}^{26}$. During the interval ${t}_{0}<t<{t}_{*}$, the fine-tuning provided by the dynamic aether took place, and at $t>{t}_{*}$, we deal with the oscillatory regime.

**Figure 4.**Illustration of the behavior of the axion perturbation function $\psi \left(\tau \right)$ in the regime of parametric excitation.

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Balakin, A.; Ilin, A.; Shakirzyanov, A.
Interaction of the Cosmic Dark Fluid with Dynamic Aether: Parametric Mechanism of Axion Generation in the Early Universe. *Symmetry* **2023**, *15*, 1824.
https://doi.org/10.3390/sym15101824

**AMA Style**

Balakin A, Ilin A, Shakirzyanov A.
Interaction of the Cosmic Dark Fluid with Dynamic Aether: Parametric Mechanism of Axion Generation in the Early Universe. *Symmetry*. 2023; 15(10):1824.
https://doi.org/10.3390/sym15101824

**Chicago/Turabian Style**

Balakin, Alexander, Alexei Ilin, and Amir Shakirzyanov.
2023. "Interaction of the Cosmic Dark Fluid with Dynamic Aether: Parametric Mechanism of Axion Generation in the Early Universe" *Symmetry* 15, no. 10: 1824.
https://doi.org/10.3390/sym15101824