ISW Signal

The Integrated Sachs-Wolfe effect records CMB photon energy changes as they traverse evolving gravitational potentials — photons climbing out of a deepening well lose energy, while those crossing a shallowing well gain it. ΛCDM predicts a specific ISW amplitude tied to dark energy's effect on potential evolution since z ≈ 1. The observed ISW signal, measured through CMB-galaxy cross-correlation, is consistently lower than predicted in some analyses and higher in others, with the sign of anomaly depending on the void versus cluster environment. SCT resolves this naturally: the dynamical cosmological term Λ_eff(x,t) is spatially varying, being enhanced in the KBC Supervoid and suppressed within dense clusters. Gravitational potentials in void regions therefore decay faster than ΛCDM predicts, while cluster potentials decay more slowly, producing an environment-dependent ISW amplitude that averages to a different total than ΛCDM's uniform Λ calculation.

Furthermore, SCT's gravitational superposition mechanism — the constructive overlap of nested comoving frame gravitational fields — adds an effective gravitational contribution in dense regions above what discrete mass counting alone would predict. This additional gravitational influence retards potential decay in clusters and filament nodes, systematically suppressing the ISW contribution from those regions. The net cross-correlation signal between the CMB and galaxy surveys therefore reflects the competition between enhanced void-ISW and suppressed cluster-ISW, naturally explaining why different survey geometries and redshift slices return apparently contradictory ISW amplitudes. No new fields are required; the entire effect emerges from GR applied to the spatially inhomogeneous Λ_eff profile and the superposition of overlapping frame gravitational wells.