Table 3.
Priors and posterior results for all models.
| Parameter | Prior | KV450 |
Planck |
||||
|---|---|---|---|---|---|---|---|
| ℋ0 | ℋ1 | 𝒯1 | ℋ0 | ℋ1 | 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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