A Density-Switched Repulsion Among Early Massive Black Holes Can Seed a Cosmic Chain (No Dark Matter Required)

We propose and test a toy-model in which high-density pockets of primordial gas rapidlyform multiple massive black holes (MBHs). Above a critical smoothed density, MBH pairsexperience a short-range, density-switched repulsive interaction (“fifth force”) in addition togravity. This repulsion inhibits monolithic collapse and promotes a percolating, filamentarynetwork — a cosmic chain. Using 2D and 3D N-body toy simulations with pressure supportand an exponential cooling law, we quantify percolation, two-point clustering g(r), the powerspectrum P(k), graph connectivity, and nearest-neighbor statistics. Across parameters, thepercolation linking length rth closely tracks the analytic interaction scale r∗ derived froma Yukawa-like screened force via Lambert-W.Importantly, this model does not invokedark matter or any other exotic particle species; the mechanism relies only on baryonic gasproducing MBHs and an effective, density-dependent interaction between them. We releasethe data tables used in all figures.