# QCD Axion Kinetic Misalignment without Prejudice

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## Abstract

**:**

## 1. Introduction

## 2. Standard Scenario

## 3. Kinetic Misalignment Mechanism

#### 3.1. Overview

#### 3.2. Weak Kinetic Misalignment

#### 3.3. Strong Kinetic Misalignment

## 4. Axion Miniclusters

#### 4.1. Formation and Properties

#### 4.2. Growth of Structures

#### 4.3. Stripping

#### 4.4. Microlensing

## 5. Conclusions

`MiMeS`[160]. The properties of AMCs can only be assessed through more sophisticated analyzes that account for the evolution of the PQ field and require modification of existing open-source codes that are already available [28]. A similar analysis involving the implementation of a Boltzmann solver can be performed in the pre-inflationary scenario, where the KM regime would be additionally constrained by isocurvature fluctuations, as has been discussed in Ref. [97].

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Standard scenario.

**Left panel**: Axion relic abundance for ${f}_{a}={10}^{15}\phantom{\rule{0.166667em}{0ex}}$GeV, taking ${\dot{\theta}}_{i}=0$.

**Right panel**: Misalignment angle required to match the whole observed DM abundance. The two lines show the comparison between numerical (solid black) and analytical (dotted blue).

**Figure 2.**Weak KM. Axion relic abundance for ${f}_{a}={10}^{15}\phantom{\rule{0.166667em}{0ex}}$GeV.

**Left panel**: ${\theta}_{i}=1$ (black) and ${\theta}_{i}=0$ (blue) for ${Y}_{\theta}>0$.

**Right panel**: ${Y}_{\theta}>0$ (black) and ${Y}_{\theta}<0$ (blue), for ${\theta}_{i}=1$. We show a comparison between numerical results (solid) and the analytical approximation with a quadratic QCD axion potential (dotted). The dashed red line shows the limit of strong KM.

**Figure 3.**Kinetic misalignment. Parameter space that reproduces the whole observed DM abundance for ${f}_{a}={10}^{15}\phantom{\rule{0.166667em}{0ex}}$GeV (

**Left**) and ${f}_{a}={10}^{12}\phantom{\rule{0.166667em}{0ex}}$GeV (

**Right**). Black and blue lines correspond to ${Y}_{\theta}>0$ and ${Y}_{\theta}<0$, respectively.

**Figure 4.**Weak kinetic misalignment.

**Left panel**: Yield ${Y}_{\theta}$ as a function of the DM axion mass ${m}_{a}$, for the values of the initial misalignment angle ${\theta}_{i}=0$ (blue) and ${\theta}_{i}=1$ (black).

**Right panel**: $\left|{Y}_{\theta}\right|$ as a function of the DM axion mass ${m}_{a}$, assuming ${\theta}_{i}=1$ and considering either ${Y}_{\theta}>0$ (black) or ${Y}_{\theta}<0$ (blue). In both panels, the red dotted line separates the regimes of weak (to left) and strong (to right) KM.

**Figure 5.**The temperature of the primordial plasma at the onset of axion field oscillations ${T}_{\mathrm{osc}}$ as a function of the axion mass. The tilted dotted line corresponds to the cases of standard misalignment or weak KM regimes in Equation (13), while the horizontal dotted line is the result in the strong KM regime in Equation (26).

**Figure 6.**The characteristic minicluster mass, for $\delta =1$. The two dotted lines correspond to the cases of standard scenario or the weak KM regime, and to the strong KM regime.

Mechanism | Initial Velocity | Oscillation Temperature |
---|---|---|

Standard scenario | ${\dot{\theta}}_{i}=0$ | $3H\left({T}_{\mathrm{osc}}^{\mathrm{mis}}\right)=m\left({T}_{\mathrm{osc}}^{\mathrm{mis}}\right)$ |

Weak KM | ${\dot{\theta}}_{i}\ne $ 0 | $3H\left({T}_{\mathrm{osc}}^{\mathrm{mis}}\right)=m\left({T}_{\mathrm{osc}}^{\mathrm{mis}}\right)$ |

Strong KM | ${\dot{\theta}}_{i}\ne 0$ | $\left|\dot{\theta}\left({T}_{\mathrm{osc}}^{\mathrm{skm}}\right)\right|=2\phantom{\rule{0.166667em}{0ex}}m\left({T}_{\mathrm{osc}}^{\mathrm{skm}}\right)$ with $\left|\dot{\theta}\left({T}_{\mathrm{osc}}^{\mathrm{mis}}\right)\right|>2\phantom{\rule{0.166667em}{0ex}}m\left({T}_{\mathrm{osc}}^{\mathrm{mis}}\right)$ |

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**MDPI and ACS Style**

Barman, B.; Bernal, N.; Ramberg, N.; Visinelli, L.
QCD Axion Kinetic Misalignment without Prejudice. *Universe* **2022**, *8*, 634.
https://doi.org/10.3390/universe8120634

**AMA Style**

Barman B, Bernal N, Ramberg N, Visinelli L.
QCD Axion Kinetic Misalignment without Prejudice. *Universe*. 2022; 8(12):634.
https://doi.org/10.3390/universe8120634

**Chicago/Turabian Style**

Barman, Basabendu, Nicolás Bernal, Nicklas Ramberg, and Luca Visinelli.
2022. "QCD Axion Kinetic Misalignment without Prejudice" *Universe* 8, no. 12: 634.
https://doi.org/10.3390/universe8120634