SAG-EFM Revised: Vainshtein-Screened Completion

This version presents a revised formulation of the Scalar Attractor Gravity — Entropic Flow Model (SAG-EFM), addressing a limitation in the original screening mechanism.

In the initial monograph, scalar-field screening was implemented using a density-dependent (Chameleon-type) mechanism. Further analysis shows that this approach leads to inconsistencies at cosmological scales, particularly in large-scale structure observables such as the growth rate fσ₈, the kinematic Sunyaev–Zel’dovich (kSZ) velocity field, and the E_G parameter.

To resolve this, the present version replaces density-based screening with a derivative (Vainshtein) screening mechanism, introducing nonlinear self-interactions in the S-field. This produces a scale-dependent modification of gravity with the following behavior:

• Cosmological scales: μ(k,z) → 1, recovering General Relativity

• Galactic scales: μ(k,z) > 1, enabling enhanced gravitational effects without particle dark matter

This modification restores consistency with current observational constraints while preserving the successful galaxy-scale phenomenology of the original framework.

This document serves as a targeted correction to the cosmological sector of the SAG-EFM framework and represents the current working formulation of the theory. The original version remains available for reference within the version history.