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), and XXIV (Kibble-Zurek production) into a unified timeline from inflation through recombination and late-time acceleration. We construct the master chronology: inflation is driven by the Hopf vacuum phase transition, yielding $n_s = 0.967$ and $r = 0.003$ conditional on an assumed Starobinsky-type effective potential (not yet derived from first principles); reheating populates the soliton spectrum via the Kibble-Zurek mechanism; baryogenesis proceeds through CP-violating nucleation at $T \sim$ MeV; dark matter freezes out as neutral $H = 0$ solitons; 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). Systematic consistency checks reveal no fatal tensions between the individual papers, though the dark matter mass presents a significant internal discrepancy: the cosmological abundance requires $m_\text{DM} \sim 2.9$ GeV, while the lightest computed $H = 0$ knot (trefoil) has mass $\sim 2$ MeV -- a factor of $\sim 1{,}450$. The phase transition order is the largest qualitative uncertainty. Two free parameters ($\epsilon_h$, $T_c$) govern the entire cosmological history, compared to six independent parameters in $\Lambda$CDM.