Cosmological Soliton Production via the Kibble-Zurek Mechanism
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2026
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| author | Novickis, Alexander |
| author_facet | Novickis, Alexander |
| contents | <div> <h4>Abstract</h4> <p>We apply the Kibble-Zurek mechanism to the cosmological production of Hopf solitons during the $\mathrm{SO}(4) \to \mathrm{SO}(3)$ symmetry-breaking phase transition of the $S^3$-valued order parameter field. The critical exponents of the 3D $\mathrm{O}(3)$ Heisenberg universality class ($\nu = 0.7112$, $z = 2.0 \pm 0.1$, Model A dynamics) --- established by finite-$T$ RG analysis (Skyrme term RG-irrelevant, $U(1)$ Hopf fiber gapped) and Hohenberg-Halperin classification (Hopf charge is topological, not Noether; no conserved slow modes couple to the order parameter) --- determine the freeze-out correlation length $\hat{\xi} = \xi_0(\tau_Q/\tau_0)^{\nu/(1+\nu z)}$, setting the defect density $n_\text{defect} \sim \hat{\xi}^{-3}$. With the cosmological quench rate $\tau_Q^{-1} \sim H(T_c) \sim T_c^2/M_P$, the resulting soliton density combined with the CP-violating asymmetry $\epsilon_h \sim 2.4 \times 10^{-5}$ (Paper IX) yields $\eta \sim 6 \times 10^{-10}$ for $T_c \sim 0.1\text{--}10$ GeV (illustrative range; the computed $T_c \sim 5.5 \times 10^{16}$ GeV from Paper XXII shifts the quantitative picture --- see Section 3). Soliton-antisoliton annihilation freezes out when $\Gamma_\text{ann} < H(T)$, leaving baryonic asymmetry from charged ($H = \pm 1$) solitons and dark matter from neutral ($H = 0$) solitons (Paper VI). The ratio $\Omega_\text{DM}/\Omega_b \sim 5$ emerges naturally in the asymmetric dark matter scenario.</p> <p>[!note] Honesty Statement The KZ scaling is robust and model-independent given the universality class, but the transition temperature $T_c$ is not derived from first principles within the soliton framework --- it is a free parameter constrained by self-consistency with observed $\eta$ and $\Omega_\text{DM}$.</p> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>cosmology</span> <span>Kibble Zurek</span> <span>topological defect</span> <span>baryon</span> <span>dark matter</span> <span>soliton</span> <span>phase transition</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-03-25</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19163290">10.5281/zenodo.19163290</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19227928 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Cosmological Soliton Production via the Kibble-Zurek Mechanism Novickis, Alexander physics cosmology Kibble-Zurek topological-defect baryon dark-matter soliton phase-transition <div> <h4>Abstract</h4> <p>We apply the Kibble-Zurek mechanism to the cosmological production of Hopf solitons during the $\mathrm{SO}(4) \to \mathrm{SO}(3)$ symmetry-breaking phase transition of the $S^3$-valued order parameter field. The critical exponents of the 3D $\mathrm{O}(3)$ Heisenberg universality class ($\nu = 0.7112$, $z = 2.0 \pm 0.1$, Model A dynamics) --- established by finite-$T$ RG analysis (Skyrme term RG-irrelevant, $U(1)$ Hopf fiber gapped) and Hohenberg-Halperin classification (Hopf charge is topological, not Noether; no conserved slow modes couple to the order parameter) --- determine the freeze-out correlation length $\hat{\xi} = \xi_0(\tau_Q/\tau_0)^{\nu/(1+\nu z)}$, setting the defect density $n_\text{defect} \sim \hat{\xi}^{-3}$. With the cosmological quench rate $\tau_Q^{-1} \sim H(T_c) \sim T_c^2/M_P$, the resulting soliton density combined with the CP-violating asymmetry $\epsilon_h \sim 2.4 \times 10^{-5}$ (Paper IX) yields $\eta \sim 6 \times 10^{-10}$ for $T_c \sim 0.1\text{--}10$ GeV (illustrative range; the computed $T_c \sim 5.5 \times 10^{16}$ GeV from Paper XXII shifts the quantitative picture --- see Section 3). Soliton-antisoliton annihilation freezes out when $\Gamma_\text{ann} < H(T)$, leaving baryonic asymmetry from charged ($H = \pm 1$) solitons and dark matter from neutral ($H = 0$) solitons (Paper VI). The ratio $\Omega_\text{DM}/\Omega_b \sim 5$ emerges naturally in the asymmetric dark matter scenario.</p> <p>[!note] Honesty Statement The KZ scaling is robust and model-independent given the universality class, but the transition temperature $T_c$ is not derived from first principles within the soliton framework --- it is a free parameter constrained by self-consistency with observed $\eta$ and $\Omega_\text{DM}$.</p> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>cosmology</span> <span>Kibble Zurek</span> <span>topological defect</span> <span>baryon</span> <span>dark matter</span> <span>soliton</span> <span>phase transition</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-03-25</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19163290">10.5281/zenodo.19163290</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
| title | Cosmological Soliton Production via the Kibble-Zurek Mechanism |
| topic | physics cosmology Kibble-Zurek topological-defect baryon dark-matter soliton phase-transition |
| url | https://doi.org/10.5281/zenodo.19227928 |