GNG f_NL Running

Beyond a simple constant f_NL, the running of non-Gaussianity with scale — how the bispectrum amplitude changes as a function of the triangle configuration wavenumber — probes the mechanism generating primordial correlations. Analyses of CMB and large-scale structure data suggest that f_NL may not be scale-independent, with hints of a positive running on large scales and suppression on smaller scales. Standard ΛCDM inflation models that generate any non-Gaussianity at all typically produce either scale-independent f_NL or specific running signatures tied to features in the inflaton potential, none of which naturally match the observed pattern. SCT's collision-generated non-Gaussianity has a characteristic scale dependence built into its mechanism: the collision geometry imprints correlations most strongly on scales comparable to the collision front thickness and the overall size of the thermalized region, with the bispectrum amplitude declining on smaller scales where the collision front's coherence is washed out by the subsequent thermalization.

The running of f_NL in SCT is therefore not a free parameter but a consequence of the collision geometry: on scales much smaller than the collision front coherence length, the local non-Gaussianity is generated primarily by nonlinear gravitational evolution from near-Gaussian initial conditions, while on scales approaching the collision geometry scale, the primordial bispectrum amplitude rises as the collision-imprinted correlations become dominant. This produces a positive running of f_NL from small to large scales — larger non-Gaussianity at longer wavelengths — which is the sign suggested by current observations. The characteristic scale at which the running turns over directly encodes the collision geometry size, providing a potential reconstruction of the original pocket collision parameters from present-day bispectrum measurements.