A new magnitude–redshift relation based on Type Ia supernovae

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Table 2.

Parameter constraints for different magnitude–redshift relations.

Relation	ℳ	b	Ω_M	Ω_Λ	w	q₀	$\hat{j_{0}}$ $Mathematical equation: $ \hat{j_0} $$
DES-SN5YR

Empirical	23.861 ± 0.010	−0.628 ± 0.021	–	–	–	–	–
Flat ΛCDM	23.857 ± 0.011	–	0.350 ± 0.017	–	–	–	–
ΛCDM	23.863 ± 0.013	–	$0 . 297_{- 0.067}^{+ 0.060}$ $Mathematical equation: $ 0.297_{-0.067}^{+0.060} $$	$0 . 566_{- 0.106}^{+ 0.093}$ $Mathematical equation: $ 0.566_{-0.106}^{+0.093} $$	–	–	–
Flat wCDM	23.865 ± 0.013	–	$0 . 273_{- 0.101}^{+ 0.070}$ $Mathematical equation: $ 0.273_{-0.101}^{+0.070} $$	–	$- 0 . 82_{- 0.16}^{+ 0.16}$ $Mathematical equation: $ -0.82_{-0.16}^{+0.16} $$	–	–
Padé	23.866 ± 0.014	–	–	–	–	$- 0 . 396_{- 0.112}^{+ 0.072}$ $Mathematical equation: $ -0.396_{-0.112}^{+0.072} $$	$0 . 664_{- 0.452}^{+ 0.851}$ $Mathematical equation: $ 0.664_{-0.452}^{+0.851} $$
Flat Padé	23.861 ± 0.011	–	–	–	–	−0.441 ± 0.024	–

Pantheon+

Empirical	23.810 ± 0.006	−0.594 ± 0.023	–	–	–	–	–
Flat ΛCDM	23.807 ± 0.007	–	0.331 ± 0.018	–	–	–	–
ΛCDM	23.810 ± 0.008	–	$0 . 298_{- 0.055}^{+ 0.053}$ $Mathematical equation: $ 0.298_{-0.055}^{+0.053} $$	$0 . 619_{- 0.084}^{+ 0.077}$ $Mathematical equation: $ 0.619_{-0.084}^{+0.077} $$	–	–	–
Flat wCDM	23.811 ± 0.009	–	$0 . 293_{- 0.073}^{+ 0.067}$ $Mathematical equation: $ 0.293_{-0.073}^{+0.067} $$	–	$- 0 . 91_{- 0.17}^{+ 0.14}$ $Mathematical equation: $ -0.91_{-0.17}^{+0.14} $$	–	–
Padé	23.809 ± 0.010	–	–	–	–	$- 0 . 492_{- 0.111}^{+ 0.069}$ $Mathematical equation: $ -0.492_{-0.111}^{+0.069} $$	$1 . 167_{- 0.502}^{+ 0.955}$ $Mathematical equation: $ 1.167_{-0.502}^{+0.955} $$
Flat Padé	23.811 ± 0.007	–	–	–	–	−0.471 ± 0.026	–

Pantheon+ (z < 1.121)

Empirical	23.812 ± 0.007	−0.606 ± 0.026	–	–	–	–	–
Flat ΛCDM	23.808 ± 0.007	–	0.336 ± 0.019	–	–	–	–
ΛCDM	23.810 ± 0.009	–	$0 . 315_{- 0.091}^{+ 0.082}$ $Mathematical equation: $ 0.315_{-0.091}^{+0.082} $$	$0 . 636_{- 0.121}^{+ 0.107}$ $Mathematical equation: $ 0.636_{-0.121}^{+0.107} $$	–	–	–
Flat wCDM	23.809 ± 0.010	–	$0 . 324_{- 0.117}^{+ 0.074}$ $Mathematical equation: $ 0.324_{-0.117}^{+0.074} $$	–	$- 0 . 97_{- 0.21}^{+ 0.22}$ $Mathematical equation: $ -0.97_{-0.21}^{+0.22} $$	–	–
Padé	23.809 ± 0.010	–	–	–	–	$- 0 . 505_{- 0.136}^{+ 0.082}$ $Mathematical equation: $ -0.505_{-0.136}^{+0.082} $$	$1 . 323_{- 0.660}^{+ 1.324}$ $Mathematical equation: $ 1.323_{-0.660}^{+1.324} $$
Flat Padé	23.811 ± 0.007	–	–	–	–	−0.468 ± 0.028	–

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