Single-field slow-roll inflation in ΛCDM predicts the local-type non-Gaussianity parameter f_NL should be of order unity or less, with a specific bispectrum-power-spectrum relation (Maldacena 2003; Bartolo 2004). LSS and CMB analyses keep finding hints, systematics-limited constraints, or mildly discrepant scale-dependent bias and bispectra preferring non-zero local f_NL (Slosar 2008; Dalal 2008). The persistent tension challenges the simple inflationary prediction.
The standard model with single-field inflation assumes f_NL near zero across all scales. Observed scale-dependent biases preferring non-zero local f_NL must be attributed to multi-field inflation, exotic primordial physics, or systematic effects. 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, primordial perturbations come from a finite multi-stage cascade rather than continuous quantum vacuum fluctuations. The cascade ran through roughly N_coll ≈ 10⁴ independent collision events (P22, P36, P37, P38) before terminating well before t ≈ 1 second (P40). Central Limit Theorem applied to that finite ensemble yields a nearly Gaussian primordial field with corrections of order 1/√N_coll.
The local-type non-Gaussianity parameter therefore comes in at f_NL ≈ 10⁻², small but in principle detectable by CMB-S4-class instruments reaching σ(f_NL) ≈ 1 and by Euclid plus SPHEREx plus LSST multi-tracer bispectrum analysis. The signal is intrinsically scale-dependent because the cascade has a hierarchy of characteristic length scales, one per cascade generation. Larger angular scales (low k) show slightly larger f_NL because they sample fewer first-stage cascade events; smaller angular scales (high k) show smaller f_NL because they sample many more daughter-stage events.
Angular momentum inheritance (P31, P32) imprints squeezed-triangle bispectrum signatures aligned with the cascade J vector, providing a directional cross-check on the cascade origin. Future surveys with σ(f_NL) < 1 will distinguish SCT (~10⁻²) from inflation (~0) and from ekpyrotic models (>5). The same cascade architecture that produces the CMB bispectrum scale-dependence (recid 27) and LSS non-Gaussianity (recid 70) produces the local f_NL hint at the predicted level.
Detection of |f_NL local| > 5 at greater than 3σ would constrain N_coll < 25, conflicting with the roughly 10⁴ events the Gaussian-spectrum derivation requires. Conversely, if f_NL is confirmed exactly zero at the 10⁻³ level by Euclid + SPHEREx multi-tracer analysis, the finite-cascade prediction is refuted in favor of strict single-field inflation.