EFC v1.3 — PPN Recovery via Density Saturation (v2.1) Page 1 GR Recovery in Energy-Flow Cosmology via Density Saturation: Quantitative PPN Analysis for the Solar System

We investigate the Solar System implications of Energy-Flow Cosmology (EFC), a framework in which late-time gravitational modifications arise from entropy-gradient effects that become suppressed in high-density regimes. We show that the Density Saturation mechanism, implemented through a screening function Θ(ρ_eff) based on a source-smoothed effective density, dynamically suppresses all EFC corrections in Solar System environments. Linearization of the modified field equations demonstrates that the leading correction acts as a scalar rescaling of Newton’s constant, preserving equality of the metric potentials Φ and Ψ and yielding the post-Newtonian parameter γ = 1 at leading order. Residual deviations are bounded by Θ(ρ_eff)·(U/c²) and are many orders of magnitude below current experimental limits from Cassini time-delay measurements, lunar laser ranging, and perihelion precession. We further show that acceleration-based screening inferred from galactic fits provides an independent suppression channel, reinforcing Solar System recovery of general relativity. While a full strong-equivalence-principle derivation requires an action-level formulation, existing bounds indicate no detectable violation at present precision. These results establish that EFC belongs to the class of screened metric theories consistent with local gravitational tests, removing a key viability obstacle and enabling meaningful cosmological tests of the framework.