On large scales the matter power spectrum should be statistically homogeneous in ΛCDM. Position-dependent power and separate-universe analyses find that local small-scale power varies more strongly with large-scale environment, direction, or location than ΛCDM with Gaussian initial conditions and linear bias predicts (Chiang 2014; Barreira 2019). The signal hints at enhanced super-sample effects or non-Gaussian couplings.
The standard model with Gaussian initial conditions assumes statistical isotropy and homogeneity at large scales. Recovering the observed large-small-scale coupling within the model requires non-Gaussian initial conditions, super-sample-variance effects, or enhanced bias modeling. None of these is parsimonious within minimal ΛCDM.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, the cascade origin produces position-dependent power as a direct geometric signature. The cascade ran through roughly N_coll ≈ 10⁴ independent collision events depositing perturbations at characteristic scales set by each cascade stage's v_rel and parent-fragment size (P22, P36, P37). Different cascade stages contribute at different scales, and their phase coherence persists through to the post-thermalization plasma evolution.
Angular-momentum inheritance (P31, P32) couples large-scale modes (J-axis-aligned) to small-scale modes through the cascade-stream filament network (P34). Modes oriented relative to the J axis carry coherent phase information across all length scales. Gravitational superposition (P50, P52) adds environmental Φ_mesh dependence, producing additional position-dependent power excess in cluster-scale environments where the coherent mesh contribution is largest. The Plasma Equivalence Theorem (P29, P30) preserves the cascade-epoch position-dependent structure through to the present day.
Predicted excess at intermediate k of roughly 5 to 15%, correlated with environmental density. The same M2 framework that produces the bispectrum scale-dependence (recid 27, 70) and the CMB curvature mode coupling (recid 33) produces the position-dependent power signature in LSS. There is no need to invoke non-Gaussian initial conditions or enhanced super-sample-variance modeling.
If precision DESI + Euclid + SPHEREx stratified position-dependent power analyses find no large-small-scale coupling beyond standard nonlinear evolution at the 1% level, the M2 cascade-imprint explanation is refuted. The signature SCT prediction is environmentally correlated 5 to 15% excess at intermediate k, with directional dependence on the cascade J axis.