Filament Length-Shear Scaling

Cosmic filaments connecting galaxy clusters are observed to follow empirical scaling relations between their length, their enclosed mass, and the shear field along their spines. These scaling relations encode information about how filaments form and persist, and deviations from ΛCDM predictions in the length-shear relation suggest that filaments are either longer, more coherent, or carry higher angular momentum than standard structure formation produces. SCT provides a natural explanation through angular momentum inheritance: every filament in the cosmic web descends from the collision geometry, and the angular momentum deposited by the collision impact parameter cascades down the mass hierarchy, imparting coherent rotational support to filament spines. Longer filaments trace the primary collision axis directions and carry more of the original angular momentum per unit length, systematically increasing their coherence length relative to ΛCDM filaments that acquire angular momentum only through stochastic tidal torquing.

The gravitational superposition mechanism also contributes to the length-shear scaling: filaments that connect dense nodes receive an enhanced effective gravitational potential from the superposition of multiple nested frame gravitational wells, deepening their spines and increasing the shear signal per unit length. This means the shear amplitude along filaments is systematically elevated above what the visible mass alone would produce, and this elevation scales with filament length because longer filaments connect more massive nodes with deeper superposition contributions. The observed length-shear scaling relation is therefore a joint signature of inherited angular momentum coherence and gravitational superposition, both of which are direct predictions of SCT's collision framework rather than parameters to be calibrated.