# SU(2) Quantum Yang–Mills Thermodynamics: Some Theory and Some Applications

## Abstract

**:**

## 1. Introduction

## 2. Thermal Ground State and (Quasi-Particle) Excitations

#### 2.1. Charge-Modulus One (Anti)calorons

#### 2.2. Thermal-Ground-State Estimate: (Anti)caloron Centers vs. Peripheries

## 3. SU(2)${}_{\mathrm{CMB}}$ and the Cosmological Model

#### 3.1. The Postulate of SU(2)${}_{\mathrm{CMB}}$ Describing Thermal Photon Gases

#### 3.2. Temperature-Redshift Relation and 3D Ising Criticality

#### 3.3. Dark Matter at High Redshifts

#### 3.4. Results on TT, TE, and EE

## 4. Conclusions

## Funding

## Conflicts of Interest

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1. | We follow the convention to denote group G’s Lie algebra by g. |

2. | The holonomy of a gauge-field configuration at finite temperature relates to its Polyakov loop at spatial infinity: If this quantity coincides with an element of the center ${\mathbf{Z}}_{2}$ of the group SU(2) then one speaks of a trivial holonomy, if this is not the case then the configuration is said to be of nontrivial holonomy. |

3. | The existence of phase boundaries in the thermalised situation is irrelevant when a monochromatic plane wave is considered. |

4. | For the present CMB with ${T}_{0}={T}_{c}=2.725\phantom{\rule{0.166667em}{0ex}}$K and ${\mathsf{\Lambda}}_{\mathrm{CMB}}={10}^{-4}\phantom{\rule{0.166667em}{0ex}}$eV condition (11), when converted into an upper bound on frequency $\nu (s)$, it reads $\nu (s)\ll 220\phantom{\rule{0.166667em}{0ex}}$MHz. |

**Figure 1.**Plot of the ratios $\frac{s}{{|\varphi |}^{-1}}$ (solid), $\frac{s}{\beta}$ (dashed), and $\frac{{|\varphi |}^{-1}}{\beta}$ (dotted) versus small values of $\lambda $.

**Figure 2.**The TT power spectra (blue error bars and grey dots are 2015 Planck data, dashed line is best-fit Lambda-Cold-Dark-Matter ($\mathsf{\Lambda}$CDM) model, dotted line SU(2)${}_{\mathrm{CMB}}$, also taking ${V}_{\pm}$ into account in perturbation equations (${\mathrm{SU}(2)}_{\mathrm{CMB}}$+${V}_{\pm}$), and solid line SU(2)${}_{\mathrm{CMB}}$, only taking massless mode into account in perturbation equations (${\mathrm{SU}(2)}_{\mathrm{CMB}}$).

**Figure 3.**Scatter plots of ${H}_{0}$ for fitted parameter values, requiring that ${\chi}^{2}<\mathrm{21,700}$ (best-fit: ${\chi}^{2}=\mathrm{21.192.6}$ for ${\mathrm{SU}(2)}_{\mathrm{CMB}}$, ${\chi}^{2}=\mathrm{20,940.1}$ for ${\mathrm{SU}(2)}_{\mathrm{CMB}}$+${V}_{\pm}$). Crosses and dots refer to ${\mathrm{SU}(2)}_{\mathrm{CMB}}$+${V}_{\pm}$ and ${\mathrm{SU}(2)}_{\mathrm{CMB}}$, whose best-fit parameter values are indicated by a solid triangle and a solid square, respectively.

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Hofmann, R.
SU(2) Quantum Yang–Mills Thermodynamics: Some Theory and Some Applications. *Universe* **2018**, *4*, 132.
https://doi.org/10.3390/universe4120132

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Hofmann R.
SU(2) Quantum Yang–Mills Thermodynamics: Some Theory and Some Applications. *Universe*. 2018; 4(12):132.
https://doi.org/10.3390/universe4120132

**Chicago/Turabian Style**

Hofmann, Ralf.
2018. "SU(2) Quantum Yang–Mills Thermodynamics: Some Theory and Some Applications" *Universe* 4, no. 12: 132.
https://doi.org/10.3390/universe4120132