Paper XXXIX: Soliton Cosmology — From Reheating to Recombination

Abstract

The topological soliton framework provides natural mechanisms for each major epoch of cosmological history, yet these mechanisms have been developed in separate papers with limited cross-checking of mutual consistency. This paper synthesizes the cosmological results from Papers VI (dark matter), IX (baryogenesis), XI (dark energy), XXII (inflation), XXIII (gravitational waves), XXIV (Kibble-Zurek production), LXIV (cyclic cosmology), LXVII (vacuum condensate dark matter), and LXVIII (gravitational constant) into a unified timeline from inflation through recombination, late-time acceleration, and the speculative far future. We construct the master chronology: inflation is driven by the Hopf vacuum phase transition with derived effective potential $V(\psi) = V_0(1 - e^{-\sqrt{2/3}\,\psi/M_P})^{2\beta}$ from the $O(3)$ Heisenberg universality class and $S^3$ KK kinetic term (Paper_XXII_Inflation|Paper XXII Section 8), yielding $n_s = 0.967$ and $r = 0.003$; reheating populates the soliton spectrum via the Kibble-Zurek mechanism with $O(3)$ critical exponents ($\nu = 0.7112$, $z = 2.0$, $\sigma_\text{KZ} = 0.881$); baryogenesis proceeds through CP-violating nucleation at $T \sim$ MeV; dark matter arises as the knotting sector of the topological vacuum condensate, predicting $\rho_\text{DM}/\rho_\Lambda = 3/8 = 0.375$ (observed: 0.387, 3.2% match) with zero free parameters; BBN proceeds with $\Delta N_\text{eff} = 0.042$ per dark species; the CMB is consistent with standard $\Lambda$CDM using the soliton-derived cosmological constant ($\rho_\Lambda$ within 1.4% of observed, though with large systematic uncertainties). The gravitational constant $G = (17/13)\alpha^{21}\hbar c/m_e^2$ (0.12% accuracy, Paper LXVIII) eliminates $M_P$ as an independent parameter. Under the vacuum condensate dark matter picture, the effective parameter count is reduced to ~4 ($\varepsilon_h$, $H_0$, $\tau$, $A_s$) vs $\Lambda$CDM's 6, with the primordial helicity $\varepsilon_h$ as the only particle-physics free parameter. In the far future, Coleman-De Luccia tunneling from the Berger vacuum to the symmetric $S^3$ dissolves all topological structure; the resulting unstable hilltop re-squashes, creating a new cycle of matter via the Kibble-Zurek mechanism (Paper LXIV).