Internal Elasticity Cosmology – Stage 4 Dark matter as topological vortices and macroscopically entangled states of the quantum-coherent elastic field ϕ

Internal Elasticity Cosmology (IEC), developed in Stages 1–3, has demonstrated that asingle quantum-coherent scalar field ϕ —representing the collective elastic displacement ofthe vacuum— simultaneously explains late-time cosmic acceleration and the observed suppression of structure growth, resolving the σ8 and H0 tensions with a single new couplingη ≃ 0.0478. In this work —Stage 4— we complete the unification by demonstrating thatcold dark matter itself emerges as stable topological vortices and macroscopically entangledconfigurations of the same elastic field ϕ. Using the post-recombination effective theory derived in Stage 3, we construct global vortex solutions with winding numbers n = ±1, ±2, . . . ,prove their topological stability, and calculate their energy-momentum tensor. The resulting density profile falls as ρv(r) ∝ 1/r2 at large radii (matching NFW for r ≫ rc) whiledeveloping a flat core of radius rc ≃ 0.5–2 kpc, naturally resolving the core-cusp problemwithout fine-tuning. Vortex–vortex interactions are logarithmic in 2+1 dimensions, generating flat rotation curves and suppressing small-scale power exactly as required by the ”missingsatellites” and ”too big to fail” problems. Numerical relaxation of random vortex networksreproduces the observed cosmic web and produces a matter power spectrum indistinguishablefrom ΛCDM at large scales, while suppressing P(k) for k ≳ 5 h Mpc−1. Macroscopic quantum coherence between vortices predicts weak but characteristic signals in 21 cm radiationand CMB polarization at very low multipoles. Internal Elasticity Cosmology thus becomesthe first genuinely unified model of dark energy and dark matter arising from a single physicalprinciple —the internal quantum elasticity of spacetime— without a cosmological constant,exotic particles, or ad-hoc modifications to general relativity