Empirical Validation of Energy-Flow Cosmology: Cluster Lensing and Galaxy Rotation Curves

AbstractWe present empirical validation of Energy-Flow Cosmology (EFC) across two distinct gravitational regimes: galaxy cluster lensing and galactic rotation curves. Using data from the Bullet Cluster (1E 0657-56), MACS J0025.4-1222, and synthetic SPARC-style galaxies, we demonstrate that EFC successfully reproduces observed gravitational phenomena without invoking dark matter particles. For cluster lensing, we show that the convergence field κ follows collisionless (stellar) matter rather than dissipative (gas) matter, with a nested model test yielding p = 0.99 for gas term irrelevance. For rotation curves, our corrected EFC model achieves χ² = 4.5 compared to χ² = 296 for pure Newtonian gravity—a 98% improvement. We discover that the entropy coupling scale λ is not a universal constant in absolute units, but the dimensionless ratio λ/R_system ≈ 0.5–1.0 appears consistent across regimes spanning five orders of magnitude in physical scale. All code and data are publicly available.