A Node-Based Energy Balance Model of Cosmological Expansion and Structure Formation

Abstract We propose a discrete node-based model of the universe in which energy (density) redistribution and local interactions govern cosmological dynamics. The model is formulated in dimensionless units with all free parameters explicitly specified. Diffusion and a Jeans-like gravitational term compete to produce cosmological expansion while allowing initial density fluctuations to grow — consistent with observed large-scale structure formation. The Hubble-like parameter H(t) is derived from mean energy density and its spatial variance, with clearly stated coefficients α = 0.8 and β = 0.3. A matter power spectrum P(k) is computed at successive times, showing power transfer from large to small scales under gravity. The dynamics are interpreted through the Four Universal Laws framework: System Integrity, Universal Balance, Causality, and the Feedback Loop Mechanism. Full simulation code is provided for reproducibility.