Tareq Gravity Model (TGM-V3): A Unified Elastic–Spacetime Framework for Galactic Dynamics, Cluster Lensing, and Cosmic Expansion

The Tareq Gravity Model (TGM-V3) is the newest and most complete formulation of the TGM framework, fully derived from the Tareq Planck Spacetime Theory (TPST).In this unified model, gravity emerges from the elastic deformation of spacetime, producing Newtonian behavior at small scales and dark-matter-like effects from curvature elasticity at large scales.TGM-V3 successfully explains: flat galactic rotation curves, gravitational lensing in merging clusters (including the Bullet Cluster), and late-time cosmic acceleration —all without invoking particle dark matter or a cosmological constant. This expanded version includes a full modern cosmology section, presenting the TPST-derived elastic expansion mode, strain-energy density, and a modified Friedmann equation: 3H2=8πG(ρm+ρelastic),3H^2 = 8\pi G\left(\rho_m + \rho_{\text{elastic}}\right),3H2=8πG(ρm+ρelastic), demonstrating that cosmic acceleration arises naturally from Planck-scale elastic strain rather than an external dark-energy component.The paper integrates observational galaxy samples, lensing predictions, and the relativistic TPST-GR extension, forming a complete alternative to ΛCDM across galactic, cluster, and cosmological scales. Email: [email protected]