The Integrated Sachs-Wolfe (ISW) effect predicts a positive cross-correlation between CMB temperature fluctuations and the foreground large-scale-structure distribution, generated as CMB photons cross evolving gravitational potentials in a dark-energy-dominated universe. Measurements consistently report ISW-LSS cross-correlation amplitudes weaker than ΛCDM constant-Λ predictions, with substantial scatter between surveys (Crittenden & Turok 1996; Giannantonio 2012; Hang 2021).
The standard model assumes constant Λ produces a uniform spatial rate of late-time gravitational-potential decay. That uniform decay rate generates a definite ISW signal amplitude when convolved with the foreground matter distribution. A weaker observed signal demands either lower σ₈ (worsening the S₈ tension), modified gravity, or unaccounted-for survey systematics.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, Λ_eff(x,t) becomes a dynamical field rather than a constant. The implication for the ISW signal is direct. If Λ_eff varies environmentally (P17, P19), the rate at which gravitational potentials decay also varies environmentally. Potentials in voids decay faster (because Λ_eff is locally enhanced); potentials in overdense regions decay more slowly (because Λ_eff is locally suppressed). The integrated ISW signal averages over this spatial variability rather than expressing a single uniform decay rate.
Spatial averaging of a non-uniform field naturally produces a lower mean amplitude than the constant-field prediction would. Some sightlines pass mostly through voids and pick up a strong ISW signal; some sightlines pass mostly through overdensities and pick up a weak signal; the cross-correlation with the LSS distribution weights these contributions in a way that does not perfectly align with the ΛCDM template. The result: lower-than-predicted ISW × LSS amplitude, with inter-survey scatter that reflects which regions of the Λ_eff landscape each survey sampled. Both features are direct M5 predictions.
Void-direction surveys are particularly affected because voids carry the strongest local Λ_eff enhancement and therefore the strongest deviation from the global average. This is consistent with the observation that void-stacking ISW analyses tend to show larger deviations from ΛCDM expectations than full-sky cross-correlations. The void-direction signal is sampling the regime where M5 effects are largest.
The same field-equation extension that resolves the Hubble tension, S₈ tension, evolving-w(z) signal in DESI, and angular-diameter-distance shape produces the ISW deficit naturally. None of these tensions requires its own separate fix. They are all surface manifestations of the same dynamical-Λ_eff mechanism that emerges once the hot-dense-center assumption is replaced with the SCT collision-and-thermalized-debris-field framework.
If a precision ISW × LSS cross-correlation survey reaches the full ΛCDM-predicted amplitude with no inter-survey scatter and no void-direction enhancement of the deviation, the M5 dynamical-Λ_eff explanation is refuted. Specifically, if the cross-correlation amplitude in void-dominated sightlines matches the cluster-dominated sightlines after standard kinematic corrections, the spatial-variability prediction fails.