SFT Self-Tuning and dRGT Coherence: The Composite Model for Emergent Gravity

The massive gravity theory of de Rham-Gabadadze-Tolley (dRGT) provides a consistent ghost-free extension to General Relativity, although its physical viability is frequently challenged by the required fine-tuning of its potential coefficients. This work addresses this naturalness problem through the Composite Model for Emergent Gravity (CMEG), formulating the ghost-free structure as a thermodynamic consequence of the non-perturbative String Field Theory (SFT) vacuum, rather than an ad hoc phenomenological ansatz. We present a systematic theoretical and computational analysis of this framework. We establish that a geometric ``primordial lattice'' emerges as the energetically favored ground state following tachyon condensation. Utilizing the BFV-BV formalism, we demonstrate that SFT gauge invariance naturally enforces a self-tuning mechanism that analytically fixes the dRGT coefficients, identifying the transverse scaling parameter 0. 0422 as an asymptotic invariant. The gravitational substrate is modeled as a Face-Centered Cubic (FCC) lattice, mapping the macroscopic vacuum density to the site percolation threshold (pc 0. 189). A massless spin-1 mode within the lattice spectrum is identified as the physical origin of the excitation mechanism. Phenomenologically, the model reconciles a strong microphysical coupling (g₅ 0. 65) with Solar System constraints via an active screening architecture. The intrinsic lattice rigidity (RE 10⁴) induces a dielectric suppression of the gauge sector and recovers General Relativity locally via the Vainshtein mechanism, resolving the vDVZ discontinuity. On cosmological scales, modified N-body equations indicate that a phantom-like expansion (w₀ -1. 08) couples to a volumetric drag on matter. This dynamic feedback yields a linear growth suppression of f₈ -1. 74\%, consistent with the requirements to ease the S₈ tension. Consequently, the parameter-free CMEG framework provides a theoretically constrained mechanism that addresses both the Hubble and structure growth tensions, yielding a Bayes factor of 2 B > 16. 8 relative to the standard CDM baseline.