f_NL Local Non-Gaussianity

The local-type primordial non-Gaussianity parameter f_NL measures the extent to which long-wavelength modes modulate short-wavelength power in the squeezed-limit bispectrum. Current constraints from Planck and large-scale structure surveys place f_NL close to zero but with error bars that still permit values of order unity, and hints of a non-zero f_NL in several analyses motivate explanation. ΛCDM single-field slow-roll inflation rigorously predicts f_NL of order the slow-roll parameters — effectively zero — and any significant detection would constitute a fundamental challenge. SCT generates a nonzero effective f_NL through the collision geometry without invoking multi-field inflation. The collision front's sweep of the overlap volume creates a large-scale mode — the mean density contrast between the collision axis direction and perpendicular directions — that coherently modulates the amplitude of small-scale perturbations throughout the thermalized plasma.

In SCT's framework, this effective f_NL is a geometric quantity: it measures the ratio of the collision-imprinted density contrast on the scale of the entire thermalized region to the amplitude of small-scale baryon-photon fluctuations. Because the collision geometry is fixed by the pocket parameters, the effective f_NL value is determined by the collision physics rather than being a free parameter. This produces a scale-dependent effective f_NL that is larger on scales approaching the collision geometry size and decreases toward smaller scales — a characteristic running that distinguishes it from the strictly scale-independent f_NL of standard primordial non-Gaussianity templates. The observed hints of nonzero f_NL and its apparent scale dependence are therefore natural predictions of SCT rather than challenges requiring new inflationary model building.