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Table 3.

Priors and posterior results for all models.

Parameter Prior KV450
Planck
0 1 𝒯1 0 1 𝒯1
AIA [ − 6, 6]
δz1 0.000 ± 0.039
δz2 0.000 ± 0.023
δz3 0.000 ± 0.026
δz4 0.000 ± 0.012
δz5 0.000 ± 0.011

AIA, s [ − 6, 6]
δz1, s [ − 0.3, 0.3] -
δz2, s [ − 0.3, 0.3]
δz3, s [ − 0.3, 0.3]
δz4, s [ − 0.3, 0.3]
δz5, s [ − 0.3, 0.3]

Ndata 390 390 390 390 390 390
Npara 6 12 11 6 12 11
χ2 366.8 356.4 356.1 357.5 364.5 364.4

Notes. The first six parameters are common nuisance parameters to account for overall IA amplitude and redshift offsets. The following are six test parameters introduced to account for potential differences of aforementioned parameters between the two sub-samples (see Eq. (10)). Priors shown in brackets are top-hat ranges whereas values with errors indicate Gaussian distributions. Results are the mean values of the posterior whereas the χ2 corresponds to the maximum likelihood. Two sets of results were derived, fixing cosmological parameters to either the KV450 or the Planck values (see Table 2). The test model ℋ1 contains 12 free parameters. The ‘control model’ ℋ0 ignores parameter differences between the two sub-samples and only includes 6 common parameters. The test setting 𝒯1 ignores the difference of IA signals in the two sub-samples.

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