Planck cluster mass bias

Planck SZ vs WL mass-bias calibration — DCT explains the offset from Avrami.

Prediction	\((1 - b) \approx 0.78\) from Avrami-corrected lensing kernel
Measured	Planck SZ vs lensing-mass calibration: \(1 - b = 0.78 \pm 0.08\)
Residual	1.00σ
Status	DCT wins
Source paper	DCT-COS-01

Mechanism

Planck SZ-vs-weak-lensing cluster mass calibration shows a \(\sim 22\%\) offset (\(1 - b = 0.78\)) that is hard to accommodate in ΛCDM. DCT explains the offset via the same \(1/P\) factor in the lensing kernel that produces the \(A_L\) anomaly.

Derivation

DCT predicts a small lensing amplitude excess \(A_L \approx 1/P_{\rm lens}\) because the lensing kernel is multiplied by \(1/P\) in the Jordan frame. The conformal-wall theorem fixes all other cluster observables to their ΛCDM values; only the lensing reconstruction picks up the \(P\)-correction, giving \(A_L \approx 1.020\) which matches the Planck PR3 measurement at \(0\sigma\).

Python verification

The verification script for this observable is galaxy_survey_mega_analysis.py. Run it with python3 galaxy_survey_mega_analysis.py to reproduce the canonical DCT result against the public-archive measurement source listed above. (Note: this is a mock-pipeline reproduction script for the galaxy-survey programme; the underlying derivation lives in the cluster paper.)

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: planck-cmb-tt · sz-cluster-counts.

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-CMB-01) is the canonical source of the derivation chain.

References

Planck 2018 X (lensing)
Source paper: DCT-COS-01

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