Alcock-Paczyński Scaling

The Alcock-Paczyński test uses the statistical isotropy of large-scale structures as a geometric cosmological probe: if the assumed cosmology is wrong, spherically symmetric structures appear distorted in redshift space. ΛCDM's Alcock-Paczyński constraints assume a fixed cosmological model with constant dark energy, and discrepancies between different survey analyses suggest that the inferred geometric parameters depend on which redshift slice or survey footprint is used. SCT explains this as a consequence of the spatially varying effective expansion rate. Because Λ_eff(x,t) depends on the local ratio of parent-frame mesh dissipation to local binding strength, the effective Hubble parameter and angular diameter distance relation varies across the sky — particularly between underdense void regions and dense filament nodes.

Structures traced within the KBC Supervoid subtend slightly larger angular sizes than ΛCDM expects because the local expansion rate is enhanced, while those in denser regions appear slightly compressed. The Alcock-Paczyński scaling factor therefore carries an environment-dependent correction that ΛCDM's isotropic cosmology cannot reproduce. Different surveys, which sample different fractions of void versus cluster environments depending on their sky coverage and redshift range, therefore yield systematically different Alcock-Paczyński measurements. SCT predicts that this survey-to-survey variation should correlate with the mean density of the survey volume — a testable prediction that requires no new physics, only GR applied to an inhomogeneous Λ_eff field.