Observable detail · COS
Planck 2018 + ACT DR6 joint \(S_8\)
| Prediction / mechanism | Joint Planck 2018 + ACT DR6 posterior on \(S_8\) is consistent with the CMB-extrapolated \(\Lambda\)CDM value; DCT canonical (constant-\(P_0\)) sits below. |
|---|---|
| Measured | Planck 2018 PR3 + ACT DR6 (2024) joint posterior. |
| Residual / status | \(\sim\!1.5\sigma\) tension under canonical constant-\(P_0\) |
| Status | SOFT |
| Source paper | DCT-CMB-01 |
Mechanism
CMB-extrapolated \(S_8\) from the linear growth function on the \(\Lambda\)CDM background; DCT corrects the late-time amplitude through the perturbation-level \(\mu_b, \mu_{DM}, \Sigma\) kernel.
Derivation
The derivation chain follows the cluster paper DCT-CMB-01 and reduces to the canonical DCT constants (\(P_0 = 0.851\), \(\omega_0 = 50{,}037\), \(c_{BD} = 138{,}189\), master identity \(2\omega_0 + 3 = c_{BD} \cdot P_0^2 = 100{,}077\)). See the cluster paper for the full multi-line derivation.
Methodology
| Domain | Cosmology (COS) |
|---|---|
| Input data source | See "References" below for the canonical public-archive citation. |
| Measurement procedure | The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference. |
| Acceptance threshold | HIT: residual within 1σ of measurement. SOFT: directional agreement 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 verdict pill above. |
Python verification
Verification script: cmb_analysis.py. Run with python3 cmb_analysis.py to reproduce the canonical DCT result against the public-archive measurement source listed below.
Cross-references
Related observables: s-8 · kids-legacy-s8 · des-y3-cosmic-shear.
Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.
Audit notes
This sub-page is part of the post-build-out of the observable archive (see the observable index). Verdict reflects the corpus-canonical (constant-\(P_0\)) treatment. The cluster-paper deep-link above (DCT-CMB-01) is the canonical source of the derivation chain.
References
- Planck Collaboration 2020 (PR3)
- ACT Collaboration 2024 (DR6)
- Source paper: DCT-CMB-01
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