Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

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Volume 659 (March 2022)

A&A, 659 (2022) A115

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Table 1.

Two-tailed p-values for relative homology for the datasets.

(a)

Relative homology (`NPIPE`)

		χ² (theoretical)			χ² (empirical)			Tukey depth
Res	FWHM	b₀	b₁	`EC`_rel	b₀	b₁	`EC`_rel	b₀	b₁	`EC`_rel
2048	5	0.709	0.569	0.858	0.677	0.548	0.852	0.545	0.505	0.912
1024	10	0.649	0.476	0.383	0.628	0.477	0.363	0.513	0.345	0.000
512	20	0.157	0.417	0.203	0.162	0.408	0.183	0.000	0.000	0.000
256	40	0.398	0.597	0.772	0.403	0.600	0.757	0.253	0.498	0.642
128	80	0.356	0.205	0.563	0.383	0.187	0.555	0.267	0.000	0.730
64	160	0.389	0.494	0.768	0.402	0.468	0.747	0.443	0.385	0.755
32	320	0.022	0.003	0.001	0.028	0.013	0.002	0.000	0.000	0.000
16	640	0.975	0.002	0.203	0.982	0.035	0.227	0.973	0.000	0.440

(b)

Relative homology (`FFP10`)

		χ² (theoretical)			χ² (empirical)			Tukey depth
Res	FWHM	b₀	b₁	`EC`_rel	b₀	b₁	`EC`_rel	b₀	b₁	`EC`_rel

threshold = 0.90

2048	5	0.431	0.566	0.890	0.397	0.537	0.900	0.000	0.360	0.000
1024	10	0.728	0.525	0.712	0.743	0.533	0.727	0.547	0.477	0.647
512	20	0.146	0.688	0.408	0.137	0.687	0.397	0.000	0.490	0.000
256	40	0.338	0.498	0.636	0.313	0.490	0.650	0.000	0.370	0.000
128	80	0.080	0.304	0.160	0.067	0.327	0.190	0.000	0.000	0.000
64	160	0.424	0.367	0.853	0.407	0.353	0.880	0.000	0.000	0.000
32	320	0.116	0.159	0.050	0.140	0.170	0.057	0.000	0.327	0.000
16	640	0.935	0.000	0.014	0.933	0.003	0.023	0.910	0.000	0.000

Notes. The p-values are obtained via the parametric (Mahalanobis distance) and non-parametric (Tukey depth) tests, for different resolutions and smoothing scales for the NPIPE (panel a) and the FFP10 (panel b) dataset. Marked in boldface are p-values 0.05 or smaller.

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