Environment-Dependent Scalar–Tensor Modified Gravity (TGM)

This work presents a phenomenological scalar–tensor modified gravity framework in which a chameleon-like scalar field interacts with local spin-density (“holes”) and large-scale curvature environments. The model, referred to as the Tareq Gravity Model (TGM), introduces an environmental coupling between the scalar field and the angular-momentum distribution of astrophysical structures. The purpose of this framework is to connect local gravitational behavior, galaxy-scale dynamics, and large-scale cosmic expansion without invoking particle dark matter or a cosmological constant. The approach integrates four major physical ideas: 1. Environmental Screening:The scalar field becomes heavy in dense regions and light in low-density regions, naturally recovering General Relativity in the Solar System while allowing modifications on galactic and cosmological scales. 2. Galaxy Rotation Dynamics:A spin-dependent scalar gradient introduces an additional long-range acceleration term, capable of producing flattened galaxy rotation curves without requiring dark matter halos. 3. Curvature Wells (“Holes”):Spin-density distributions deepen the effective scalar potential, shifting its minimum and altering the scalar mass. These “holes” define local scalar environments that shape rotational and gravitational behavior. 4. Cosmic Acceleration:A cumulative “hole energy density” term, ρ_hole(t), may contribute to late-time accelerated expansion through the large-scale distribution of spin-induced curvature wells. This work also provides conceptual foundational equations that formalize these effects, including a modified effective potential, spin-density field, screening correction, scalar-driven rotation curve formula, and the hole contribution to expansion dynamics. A critique–response section addresses common theoretical questions, and a toy-model rotation curve is included to illustrate the scalar contribution relative to Newtonian expectations. This version includes the finalized and corrected PDF (Version 1.0 of the paper), replacing the earlier preliminary draft. It incorporates the foundational equations, explanation section, critique–response discussion, and the demonstration rotation curve.