Planck EE polarization (τ)

CMB EE polarization optical depth — DCT inherits SM at recombination.

Prediction	\(\tau = 0.0544 \pm 0.0073\) (Planck PR3 reionisation peak fit; SM)
Measured	\(\tau = 0.054 \pm 0.007\) (Planck PR3)
Residual	0.0σ
Status	Tied
Source paper	DCT-CMB-01

Mechanism

DCT inherits ΛCDM at recombination through the conformal-wall theorem: the tie field is locked to \(P = 1\) in the radiation-dominated era, so the linear-perturbation transfer function and the acoustic peaks reduce to the standard ΛCDM forms. Late-time deviations enter only through the Jordan-frame redshift–distance relation, which leaves the angular-power spectrum invariant.

Derivation

The conformal-wall theorem (DCT-CMB-01) shows that the tie-field background is locked to \(P = 1\) in the radiation-dominated era. The CMB transfer function reduces to the standard ΛCDM form, with the angular acoustic scale, peak heights, and damping tail all matching ΛCDM exactly. Late-time \(P\)-corrections enter only through the Jordan-frame distance ladder.

Python verification

The verification script for this observable is cmb_analysis.py. Run it with python3 cmb_analysis.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: reionization-history · planck-cmb-tt.

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 VI cosmological parameters
Source paper: DCT-CMB-01

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