# Baryon-Antibaryon Annihilation in the Evolution of Antimatter Domains in Baryon-Asymmetric Universe

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## Abstract

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## 1. Introduction

## 2. Cosmological Scenario

## 3. Symmetry-Breaking Scenario

#### 3.1. Spontaneous CP Violation

#### 3.2. Spontaneous Baryosynthesis

## 4. Antimatter Domains and Antibaryon Interactions

**radiation-dominated era**, within the cosmological evolution, the dominant contribution to the total energy is due to photons.

**matter-dominated era and following**, within a non-homogeneous scenario, the following description holds:

## 5. Space-Time Antimatter Statistical Distribution for Low-Density Antimatter Domains

#### 5.1. Low-Density Antimatter Domains Described by a Binomial Space-Time Statistical Distribution

#### 5.2. Low-Density Antimatter Domains Described by a Bernoulli Space-Time Statistical Distribution

#### 5.3. Low-Density Antimatter Domains Described by a Poisson Space-Time Statistical Distribution

#### 5.4. Low-Density Antimatter Domains Described by a Gaussian Space-Time Statistical Distribution

## 6. Nucleon-Antinucleon Interaction Studies: Boundary Interactions

#### 6.1. A Study: Proton-Antiproton Annihilation Probability, Limiting Process-Theoretical Formulation

#### 6.2. Nucleon-Antinucleon Interaction (Annihilation) Probabilities: Limiting Process-Theoretical Formulation

#### 6.3. Further Specifications of Boundary Intertactions

#### 6.4. An Example

## 7. Observational Evidence

## 8. Equation for the Number Density of Antiprotons

#### 8.1. Time Evolution of Antimatter Domains

#### 8.2. Number of Antibaryons in the Boundary Spherical Shell in Which the Antibaryon-Baryon Interaction Takes Place

#### 8.3. Perfect-Fluid Solution(s)

**perfect-fluid solution**can be taken into account, i.e., a perfect-fluid solution

#### 8.4. Plasma Characterization

#### 8.4.1. Turbulent Regime

#### 8.4.2. Viscosity Coefficient

#### 8.5. Chemical-Potential Characterization

## 9. Two-Point Correlation Functions

#### 9.1. Davis–Peebles Estimator

**Davis–Peebles estimator**is used for the correlation function for an antimatter domain and another object.

#### 9.2. Analytical Solution of the Davis–Peebles Estimator

#### 9.3. Hamilton Estimator

**Hamilton estimator**${\tilde{\xi}}_{l,{l}^{\prime}}$ accounts for the difference in (coordinate) distances among the Binomial antimatter spacetime distribution and the Poisson antimatter spacetime distribution.

## 10. Outlook and Perspectives

## 11. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Khlopov, M.Y.; Lecian, O.M.
Baryon-Antibaryon Annihilation in the Evolution of Antimatter Domains in Baryon-Asymmetric Universe. *Universe* **2021**, *7*, 347.
https://doi.org/10.3390/universe7090347

**AMA Style**

Khlopov MY, Lecian OM.
Baryon-Antibaryon Annihilation in the Evolution of Antimatter Domains in Baryon-Asymmetric Universe. *Universe*. 2021; 7(9):347.
https://doi.org/10.3390/universe7090347

**Chicago/Turabian Style**

Khlopov, Maxim Y., and Orchidea Maria Lecian.
2021. "Baryon-Antibaryon Annihilation in the Evolution of Antimatter Domains in Baryon-Asymmetric Universe" *Universe* 7, no. 9: 347.
https://doi.org/10.3390/universe7090347