Bispectrum Non-Gaussianity Scale-Dependence

Primordial non-Gaussianity, quantified through the CMB bispectrum, encodes interactions in the primordial density field beyond the two-point power spectrum. ΛCDM with single-field slow-roll inflation predicts an extremely small non-Gaussianity parameter f_NL consistent with zero; observed hints of scale-dependent bispectrum signal exceeding this prediction remain unexplained. In SCT, non-Gaussianity is a natural consequence of the collision geometry. The superluminal collision front swept a finite-thickness boundary between the two incoming pockets. Within this boundary layer, the energy density was modulated by the relative phase of the two pocket interiors — regions of constructive gravitational superposition received more energy deposition than regions of partial cancellation. This spatially correlated energy modulation is intrinsically non-Gaussian because it reflects a coherent geometric pattern rather than uncorrelated Gaussian fluctuations.

The scale-dependence of the bispectrum in SCT arises because the collision geometry has a preferred scale — the collision front thickness and the two pocket sizes — that introduces characteristic angular momentum and energy deposition length scales. Modes with wavelengths comparable to the collision front thickness are maximally affected by the non-Gaussian modulation, while modes much larger than the pocket scale or much smaller than the front thickness approach Gaussian statistics. This scale-dependent non-Gaussianity is fully consistent with GR and requires no inflaton self-coupling; it is a projection of the three-dimensional collision geometry onto the two-dimensional CMB sky, mediated by the angular momentum inheritance that organized the matter distribution after thermalization.