Structural Cosmology v2.2: Linear Perturbation Theory and the Geometry-Growth Decoupling Prediction

Structural Cosmology v2. 2 develops a linear perturbation framework for the structural field Δ, extending the effective field formulation of v2. 0 and the covariant field equations of v2. 1. Starting from the FLRW background dynamics H (t), Δ (t), and a (t), the theory introduces scalar-vector-tensor (SVT) perturbations, formulates a linearized structural field equation with a time-dependent effective mass m²ₑff (t), and derives modified gravitational observables including the effective gravitational coupling Gₑff (k, z) =Gμ (k, z) and the gravitational slip parameter η (k, z) =Φ/Ψ. The framework connects structural field perturbations to cosmological structure growth through scale- and redshift-dependent modifications of the growth factor D (k, a), growth rate f (k, z), and the observable quantity fσ₈ (k, z). A Geometry-Growth Parameter Tension (GGPT) pipeline is established, linking structural field dynamics to an illustrative prediction of Δ (fσ₈) ~ O (5%) near redshift z ~ 1–1. 5, providing a theoretical basis for the phenomenological GGPT signal previously reported in Structural Cosmology v1. 3. The work further develops a power-spectrum projection framework, introduces five perturbation-level falsifiability criteria (C31–C35), and establishes a bridge toward nonlinear structure formation, N-body modeling, and baryonic extensions planned for v2. 3. This release includes: Full v2. 2 manuscript (38 figures) Linear perturbation framework Modified gravity observables μ (k, z) and η (k, z) Growth-rate and fσ₈ analysis GGPT theoretical framework Power-spectrum projection formalism Falsifiability criteria C31–C35 Reproducible Python demonstration code All numerical examples are illustrative and intended as conceptual demonstrations of the framework rather than precision cosmological parameter estimation.