Bispectrum Non-Gaussianity Scale-Dependence

The ΛCDM Tension

Planck finds the primordial bispectrum consistent with zero in every standard template (f_NL local = -0.9 +/- 5.1; PR4: -0.1 +/- 5.0), while scale-dependent variants remain weakly constrained. Single-field inflation predicts f_NL near 0.01, untestably small; multi-field models predict anything. The sector advertised as inflation's discriminating test currently discriminates nothing: no result on the table can falsify the standard picture.

The ΛCDM Assumption That Creates It

ΛCDM attributes the fluctuations to an unspecified inflaton sector, so the bispectrum prediction is only as sharp as the model chosen, and the model space spans every observable outcome. A framework that can absorb any measured amplitude, sign, or running has surrendered the test; the data are precise, and the model has nowhere to put a prediction.

SCT Resolution: M2 (Collision Cascade Statistics)

SCT replaces the hot-dense-center with a cascade of order 10⁴ collision events (P36, P37, P38), and the three-point sector follows from counting. Summing independent deposits invokes the central limit theorem: the field is driven toward Gaussianity with residual non-Gaussianity of order 1/√N_coll, giving |f_NL| of about 10⁻². That lands squarely inside the Planck null result, and it is a derived number, not a model choice: the same N_coll that Gaussianizes the field also sets the tilt n_s = 1 - 1/L through the cascade depth.

The scale dependence is the SCT-specific fingerprint. Each cascade stage deposits power at its own characteristic scale with its own event count, and the largest scales were built by the fewest events, so the residual 1/√N statistics leave f_NL gently rising toward small wavenumbers while remaining tiny everywhere. The bispectrum is mildly scale-dependent because the cascade had stages; an inflaton needs a designed feature to mimic that, while SCT cannot avoid it.

This is the same event-counting that suppresses isocurvature modes (complete thermalization from one bath), keeps the tensor background at r below 10⁻⁵, and ties the spectral tilt to hierarchy depth: one cascade, four locked-together predictions in the primordial sector, none adjustable after the fact.

Falsifier

The registered kill runs both directions. A detection of |f_NL| above 5 at 3σ or better would force N_coll below 25, irreconcilable with the roughly 10⁴ events the n_s = 0.965 tilt requires: the cascade cannot be simultaneously shallow and deep. Conversely, CMB-S4 and 21-cm measurements reaching sigma(f_NL) near 1 and finding f_NL exactly zero at the 10⁻² level would erase the finite-event residual the cascade must leave.

Premise Grounding

#Bispectrum #NonGaussianity #fNL #ScaleDependence #PlanckCMB #CMBS4 #SPHEREx #CollisionCascade #CentralLimitTheorem #LCDMTension #SuccessiveCollisionTheory #SCT #NipokSCT #DRJMNIPOK #thenaturalstateofnature #cosmology #astrophysics