Position-Dependent Power

The amplitude of the matter power spectrum varies with position across the observable universe at a level that exceeds cosmic variance expectations for a statistically homogeneous field. This position-dependent power — detected through analyses of squeezed-limit bispectra and local variance measurements — indicates that the large-scale density environment modulates the small-scale clustering amplitude. ΛCDM's scale-invariant primordial spectrum provides no mechanism for this modulation beyond the modest coupling generated by nonlinear gravitational evolution. SCT provides a direct mechanism: the tensor mesh dissipation rate varies spatially with the parent-frame hierarchy, and regions within denser supercluster environments sit in deeper gravitational wells whose slower mesh dissipation suppresses local Λ_eff, thereby retarding local expansion and enhancing small-scale clustering amplitude above the cosmic mean.

The collision-imprinted non-Gaussian initial conditions further contribute to position-dependent power. Because the primordial density field carries the collision geometry's bispectrum, the large-scale mode associated with the collision axis directly modulates the amplitude of small-scale modes aligned with it — a form of scale-dependent bias that arises naturally from the non-Gaussian initial state rather than from any coupling between inflation modes. The position-dependent power is therefore a superposition of two SCT effects: the spatially varying Λ_eff modulating local expansion rates, and the collision-geometry bispectrum modulating small-scale mode amplitudes through large-scale mode coupling. Together these predict a specific angular pattern for position-dependent power that correlates with both the CMB anomaly axis and the KBC Supervoid geometry.