Constraints on AvERA cosmologies from cosmic chronometers and type Ia supernovae

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Table 3.

Model fit and test results for SN Ia data.

Parameter/Statistic	AvERA-135k	AvERA-320k	AvERA-625k	AvERA-1080k	Flat ΛCDM
H₀	$72 . 16_{- 1.01}^{+ 1.04}$ $72.16_{-1.01}^{+1.04}$	$72 . 06_{- 1.01}^{+ 1.05}$ $72.06_{-1.01}^{+1.05}$	$71 . 99_{- 1.03}^{+ 1.05}$ $71.99_{-1.03}^{+1.05}$	$71 . 94_{- 1.02}^{+ 1.03}$ $71.94_{-1.02}^{+1.03}$	$73 . 13_{- 1.05}^{+ 1.06}$ $73.13_{-1.05}^{+1.06}$
M_B	$- 19 . 201_{- 0.031}^{+ 0.031}$ $-19.201_{-0.031}^{+0.031}$	$- 19 . 200_{- 0.031}^{+ 0.031}$ $-19.200_{-0.031}^{+0.031}$	$- 19 . 200_{- 0.030}^{+ 0.031}$ $-19.200_{-0.030}^{+0.031}$	$- 19 . 198_{- 0.031}^{+ 0.030}$ $-19.198_{-0.031}^{+0.030}$	$- 19 . 210_{- 0.031}^{+ 0.031}$ $-19.210_{-0.031}^{+0.031}$
α	$0 . 147_{- 0.004}^{+ 0.004}$ $0.147_{-0.004}^{+0.004}$	$0 . 146_{- 0.004}^{+ 0.004}$ $0.146_{-0.004}^{+0.004}$	$0 . 146_{- 0.004}^{+ 0.004}$ $0.146_{-0.004}^{+0.004}$	$0 . 147_{- 0.004}^{+ 0.004}$ $0.147_{-0.004}^{+0.004}$	$0 . 149_{- 0.004}^{+ 0.004}$ $0.149_{-0.004}^{+0.004}$
β	$2 . 942_{- 0.073}^{+ 0.072}$ $2.942_{-0.073}^{+0.072}$	$2 . 941_{- 0.071}^{+ 0.075}$ $2.941_{-0.071}^{+0.075}$	$2 . 937_{- 0.072}^{+ 0.073}$ $2.937_{-0.072}^{+0.073}$	$2 . 951_{- 0.073}^{+ 0.073}$ $2.951_{-0.073}^{+0.073}$	$2 . 981_{- 0.073}^{+ 0.073}$ $2.981_{-0.073}^{+0.073}$
γ	$0 . 010_{- 0.011}^{+ 0.011}$ $0.010_{-0.011}^{+0.011}$	$0 . 011_{- 0.011}^{+ 0.011}$ $0.011_{-0.011}^{+0.011}$	$0 . 010_{- 0.011}^{+ 0.011}$ $0.010_{-0.011}^{+0.011}$	$0 . 009_{- 0.011}^{+ 0.011}$ $0.009_{-0.011}^{+0.011}$	$0 . 010_{- 0.011}^{+ 0.011}$ $0.010_{-0.011}^{+0.011}$
Ω_m, 0	0.332^*	0.299^*	0.279^*	0.266^*	$0 . 328_{- 0.018}^{+ 0.018}$ $0.328_{-0.018}^{+0.018}$

χ²	1539	1543	1547	1551	1521
log₁₀ℬ (NS)	2.775	3.649	4.603	5.495	0
log₁₀ℬ (AD)	0.223	0.148	0.074	0 (2.782)	0.761

Notes. Best-fit parameter values and model comparison statistics for the SN dataset. H₀ is given in kilometers per second per megaparsec. Simulated values of Ω_m, 0 values for the AvERA models (marked with asterisk) are also included for reference. The χ² values were computed using the best-fit parameters. Bayes factors are shown for both the nested sampling evidence [log₁₀ℬ (NS)] and the AD test [log₁₀ℬ (AD)], as is defined in the main text in Section 2. While none of the models satisfy the AD test’s p ≥ 0.05 criterion, the test favors the AvERA-1080k model (with ${log}_{10} p_{\max}^{- 1} = 2.782$ $\log_{10}p^{-1}_{\mathrm{max}} = 2.782$ ) and indicates a clear preference for the AvERA model over the flat ΛCDM model. This contrasts with the nested sampling Bayes factors, which strongly favor the flat ΛCDM model. The discrepancy is due to the flat ΛCDM model overfitting the SN data (see Section 3 for a detailed discussion).

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