Cosmic String Network — Kibble-Zurek Mechanism

Topological defects formed during symmetry-breaking phase transitions

ξ = 60
τ_Q = 0.50
γ = 0.005

Kibble (1976) — Zurek (1985) Mechanism

When a system undergoes a symmetry-breaking phase transition faster than the relaxation time, causally disconnected regions choose independent vacuum states. Where these regions meet, topological defects must form. For U(1) symmetry: vortices (2D) / strings (3D).

n_defects ~ ξ^{-d} , ξ_KZ ~ ξ₀ · (τ_Q/τ₀)^{ν/(1+νz)}

Strings form a random network with scale-invariant (fractal) structure. The network evolves by loop decay and intercommutation. Scaling: ρ_string ~ t⁻² (one long string per Hubble volume). Cosmic strings could seed large-scale structure — constrained by CMB to Gμ < 10⁻⁷.