Table 2.
Estimators of the consistency between our fiducial 3 × 2 pt analysis and the Planck Collaboration VI (2020) TTTEEE+lowE results.
| Metric | Reference | Value | PTE | PTE [σ] |
|---|---|---|---|---|
| τ | Eq. (8) | 3.1 | – | 3.1σ |
| dH | Eq. (G.1) | 0.95 | – | 3.1σ |
| pS | Eq. (G.3) | 0.9981 | 0.0019 | 3.1σ |
| R | Eq. (9) | 23 ± 6 | – | – |
| lnR | Eq. (G.5) | 3.1 ± 0.3 | – | – |
| lnS | Eq. (G.4) | −2.0 ± 0.1 | 0.08 ± 0.02 | 1.8 ± 0.1σ |
| QDMAP | Eq. (G.10) | 9.5 | 0.037 | 2.1σ |
| QUDM | Eq. (G.11) | 7.7 | 0.054 | 1.9σ |
Notes. The considered tension metrics are: (1) the differences between the means in S8, divided by the standard deviations added in quadrature, τ; (2) the Hellinger distance, dH, between S8 posterior distributions (Appendix G.1); (3) the fraction of the S8 parameter shift distribution that has a higher probability than no shifts (Appendix G.2); (4) the Bayes ratio R between a model that assumes a single cosmology for both our 3 × 2 pt and the Planck data, and a model that uses separate cosmologies for the two data sets; (5) the logarithm lnR of the Bayes ratio; (6) the suspiciousness lnS (Handley & Lemos 2019; 7) and (8) the concordance-discordance estimators QDMAP and QUDM (Raveri & Hu 2019). The columns list the estimator metric considered, the relevant equation reference, the measured value, and the ‘probability-to-exceed’ the measured value (PTE), under the assumption that the two data sets are consistent.
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