# Dark Energy, QCD Axion, and Trans-Planckian-Inflaton Decay Constant

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## Abstract

**:**

## 1. Introduction

## 2. On Global Symmetries

#### 2.1. The ’t Hooft Mechanism

#### 2.2. Breaking Scales

## 3. The “Invisible” Axion

**E**is pictorially shown in Figure 3.

#### 3.1. Axion Inhomogeneities in Galaxies and Mini-Clusters

#### 3.2. The Domain Wall Problem in “Invisible” Axion Models

#### 3.3. Searches of “Invisible” Axions

## 4. A BCM as Dark Energy

## 5. Inflation and Gravity Waves in the Beginning

## 6. Global Symmetries and Non-Abelian Gauge Groups

## 7. Discussion and Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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1. | With two light quarks, ${\Lambda}_{\overline{\mathrm{MS}}}^{\left(2\right)}$ is larger than ${\Lambda}_{\overline{\mathrm{MS}}}^{\left(3\right)}\phantom{\rule{0.166667em}{0ex}}$. |

2. | If ${f}_{a}$ is much lower than the above bound at the level of ${10}^{7}\phantom{\rule{0.166667em}{0ex}}$GeV, the axion condensation can convert to thermal axions [78]. |

3. | For the ${\mathrm{U}\left(1\right)}_{\mathrm{PQ}}$, the symmetry is better to be exact at tree level or almost exact toward the solution of the strong CP problem with $|\overline{\theta}|<{10}^{-10}$ as discussed in Section 3. |

4. | If the symmetry breaking is soly by the non-Abelian anomaly, then we obtain $\delta =0$. |

**Figure 3.**The resonant detection idea of the QCD axion. The

**E**-field follows the axion vacuum oscillation.

**Figure 5.**A schematic view on the gauge couplings, ${\mathrm{sin}}^{2}{\theta}_{\mathrm{W}}$, and ${\tilde{c}}_{a\gamma \gamma}$.

**Figure 6.**A horizon scale string-wall for ${N}_{\mathrm{DW}}=1$ with a small membrane bounded by string. (

**a**) A (or a few) horizon scale string(s) and a giant wall attached to it [98]; (

**b**) A huge number of small walls bounded by an axionic string which punch holes in the giant walls; (

**c**) The punched holes expand with the light velocity and eat up the giant string-walls.

**Figure 7.**Small DW balls ((

**a**,

**b**), with punches showing the inside blue-vacuum) and the horizon scale string-wall system (

**c**,

**d**) for ${N}_{\mathrm{DW}}=2$: (

**a**) a DW ball with a string loop, (

**b**) a DW ball without a string loop, (

**c**) collision with a ball of type (

**a**), and (

**d**) collision by a ball of type (

**b**). Yellow walls are $\theta =0$ walls, and yellow-green walls are $\theta =\pi $ walls. Yellow-green walls of type (

**b**) are also present.

**Figure 8.**The DE potential in the red angle-direction in the valley of radial field of height $\approx {M}_{\mathrm{GUT}}^{4}$.

**Table 1.**The coupling ${c}_{a\gamma \gamma}$ for ${c}_{a\gamma \gamma}^{0}={\tilde{c}}_{a\gamma \gamma}$ given in the KSVZ and DFSZ models. For the u and d quark masses, ${m}_{u}=0.5\phantom{\rule{0.166667em}{0ex}}{m}_{d}$ is assumed for simplicity. $(m,m)$ in the last row of KSVZ means m quarks of ${Q}_{\mathrm{em}}=\frac{2}{3}\phantom{\rule{0.166667em}{0ex}}e$ and m quarks of ${Q}_{\mathrm{em}}=-\frac{1}{3}\phantom{\rule{0.166667em}{0ex}}e$. SUSY in the DFSZ models includes contributions of color partners of Higgsinos. If we do not include the color partners, i.e., in the MSSM without heavy colored particles, ${c}_{a\gamma \gamma}\simeq 0$.

KSVZ: ${\mathit{Q}}_{\mathbf{em}}$ | ${\mathit{c}}_{\mathit{a}\mathit{\gamma}\mathit{\gamma}}$ | DFSZ: $({\mathit{q}}^{\mathit{c}},{\mathit{e}}_{\mathit{L}})$ pair | Higgs | ${\mathit{c}}_{\mathit{a}\mathit{\gamma}\mathit{\gamma}}$ |
---|---|---|---|---|

0 | $-2$ | non-SUSY $({d}^{c},{e}_{L})$ | ${H}_{d}$ | $+\frac{2}{3}$ |

$\pm \frac{1}{3}$ | $-\frac{4}{3}$ | non-SUSY $({u}^{c},{e}_{L})$ | ${H}_{u}^{*}$ | $-\frac{4}{3}$ |

$\pm \frac{2}{3}$ | $+\frac{2}{3}$ | GUTs | $+\frac{2}{3}$ | |

$\pm 1$ | $+4$ | SUSY | $+\frac{2}{3}$ | |

$(m,m)$ | $-\frac{1}{3}$ |

**Table 2.**String model prediction of ${c}_{a\gamma \gamma}$. In the last line, ${c}_{a\gamma \gamma}=(1-2{\mathrm{sin}}^{2}{\theta}_{W})/{\mathrm{sin}}^{2}{\theta}_{W}$ with

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Kim, J.E.
Dark Energy, QCD Axion, and Trans-Planckian-Inflaton Decay Constant. *Universe* **2017**, *3*, 68.
https://doi.org/10.3390/universe3040068

**AMA Style**

Kim JE.
Dark Energy, QCD Axion, and Trans-Planckian-Inflaton Decay Constant. *Universe*. 2017; 3(4):68.
https://doi.org/10.3390/universe3040068

**Chicago/Turabian Style**

Kim, Jihn E.
2017. "Dark Energy, QCD Axion, and Trans-Planckian-Inflaton Decay Constant" *Universe* 3, no. 4: 68.
https://doi.org/10.3390/universe3040068