Polymer Network Cosmology and the Dark Sector

We develop Polymer Network Cosmic Teleodynamics (PNCT), a covariant effective framework in which the cosmic web is modeled as a percolating, memory-bearing, self-gravitating network whose constitutive response is guided by viscoelastic polymer physics. Affine filament stretching, transverse tidal confinement, and nonlocal strain memory generate, respectively, an effective dark energy-like background component, environment-dependent clustering corrections, and a history-dependent teleodynamic bias functional. The central structural event is a sol-gel-like percolation transition at z * ∼ 1-2, after which a coherent spanning web stores elastic free energy and can drive late-time acceleration. The resulting effective equation of state exhibits a three-stage trajectory, including phantom-like growth near activation, phantom divide crossing as transverse coherence is lost, and relaxation toward w TD → −1 + through gravitational saturation and post-gel strand balance. The framework predicts two testable observables: synchronization between cosmic web percolation and dark sector activation, and environment-dependent growth/lensing residuals in nodes, filaments, walls, and voids. These signatures are testable with DESI, Euclid, Roman, and LSST and would distinguish PNCT from smooth dark energy models and generic scale-dependent modified gravity.