ISW effect

Integrated Sachs–Wolfe cross-correlation — DCT consistent with ΛCDM detection.

Prediction	\(C_\ell^{T\phi}\) cross-correlation; DCT \(\sim P_0\) ΛCDM late-time decay rate
Measured	Planck \(\times\) NVSS / 2MASS / WISE / SDSS
Residual	0.0σ
Status	Tied
Source paper	DCT-COS-01

Mechanism

DCT modifies the late-time gravitational-potential decay rate through the Avrami profile: \(\dot \Phi^{\rm DCT} = P_0 \dot \Phi^{\Lambda CDM}\) at \(z \sim 0.5\). The CMB-galaxy cross-correlation is rescaled by a factor \(\sim P_0\) but stays well within current statistical uncertainty.

Derivation

The growth-of-structure equation in the Jordan frame picks up a late-time correction from the Avrami profile: \(\delta'' + 2H\delta' - 4\pi G \rho_m P_{\rm eff} \delta = 0\) with \(P_{\rm eff} \to 1\) at high redshift and a mild \((1 - P_0)\) suppression at \(z = 0\). Under the canonical constant-\(P_0\) treatment this gives \(S_8 \approx 0.776\) against KiDS-Legacy 2025 \(0.815 \pm 0.022\), a \(\sim\!1.8\sigma\) tension; an interim Avrami-extended branch that closed the tension at \(S_8 = 0.811\) was reverted on (see Updates).

Python verification

The verification script for this observable is cosmology_tests.py. Run it with python3 cosmology_tests.py to reproduce the canonical DCT result against the public-archive measurement source listed above.

Methodology

Domain	Cosmology (COS)
Input data source	See "References" below for the canonical public-archive citation. The verification script consumes the published value (or the public dataset, where applicable) and compares against the DCT closed-form prediction.
Measurement procedure	The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference; no internal recalibration is applied.
Acceptance threshold	HIT: residual within 1σ of measurement. SOFT: directional agreement, residual within bracketing range. OPEN: untested or unresolved.
Falsification threshold	MISS: prediction excluded at ≥3σ by the canonical measurement under the corpus-canonical (constant-\(P_0\)) treatment.
Current status	See the verdict pill in the prediction table above.

Cross-references

Related observables in the same domain: boss-void-isw.

Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.

Audit notes

Status post-: this observable's verdict above reflects the corpus-canonical (constant-\(P_0\)) treatment. Any prior interim Avrami-extension framing has been reverted (see /updates/ for the change log). The cluster-paper deep-link above (DCT-BAO-01) is the canonical source of the derivation chain.

References

Planck 2018 VI cosmological parameters
Source paper: DCT-COS-01

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