Connectivity Statistics

The connectivity of the cosmic web — how many filaments connect to a given cluster node, and the statistical distribution of these valence numbers — is sensitive to the topology of the initial density field and the merger history of halos. ΛCDM predictions for connectivity statistics, derived from N-body simulations of Gaussian initial conditions evolved under gravity, show systematic discrepancies with observed cluster catalogs: some massive clusters appear to have more filament connections than expected, while some regions of the web are less well-connected than simulations predict. SCT resolves this through the collision geometry: the initial density field is not Gaussian but carries the non-Gaussian imprint of the pocket collision, concentrating connectivity at nodes aligned with the primary collision axis and its secondary collision fronts.

The angular momentum inheritance further organizes connectivity: nodes near the collision axis — which received more angular momentum — tend to be at the intersection of multiple filaments because they formed from the highest-density collision ejecta regions where multiple flow lines converged. Nodes far from the collision axis formed from more isotropic ejecta and tend to have lower filament valence. The resulting connectivity distribution has a fat tail toward high valence at the nodes tracing the collision geometry, while being somewhat deficient in intermediate valence nodes in underdense regions. This is precisely the pattern seen in observations — extreme connectivity at the most massive nodes and a deficit of moderately connected structures in voids — and it emerges naturally from SCT's collision topology without requiring tuned initial conditions.