Topological Integer-Winding Dark Matter: Stability from $π_2(\mathrm{SU}(3)/\mathrm{SO}(3)) = \mathbb{Z}$

Abstract

We propose a dark matter model in which the symmetry-breaking pattern SU(3)_dark -> SO(3)_dark x Z_2 produces absolutely stable point-like topological defects classified by pi_2(SU(3)/[SO(3) x Z_2]) = Z. The lightest neutral member chi^0 of the resulting dark octet couples to Standard Model fields only through a kinetic-mixing portal (g_f = 10^-3) and gravity. An extended Gell-Mann-Okubo mass operator incorporating the quantum number darkicity T_dark predicts two scale-independent mass ratios, r_21 = M(chi^++)/M(chi^0) = 1.042 +/- 0.003 and r_31 = M(Sigma^0_dark)/M(chi^0) = 0.809 +/- 0.004, falsifiable at FCC-ee. Eight coupled Boltzmann equations with co-annihilation yield Omega_DM h^2 = 0.120 at M_0 = 150 GeV. Self-interaction cross-sections satisfy all astrophysical bounds from dwarf galaxies to the Bullet Cluster. The model predicts a stochastic gravitational-wave background at f_* = 1.65 mHz (LISA, SNR = 8.5) and dark acoustic oscillations at r_DAO = 2.3 +/- 0.4 Mpc (SKA).