A new magnitude–redshift relation based on Type Ia supernovae

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Table 5.

Parameter constraints for the deep-field regions.

Region	Empirical relation		Flat ΛCDM model		Flat Padé model

	ℳ	b	ℳ	Ω_M	ℳ	q₀
S1	23.823 ± 0.029	−0.530 ± 0.059	$23 . 810_{- 0.028}^{+ 0.036}$ $Mathematical equation: $ 23.810_{-0.028}^{+0.036} $$	$0 . 273_{- 0.037}^{+ 0.049}$ $Mathematical equation: $ 0.273_{-0.037}^{+0.049} $$	$23 . 820_{- 0.028}^{+ 0.034}$ $Mathematical equation: $ 23.820_{-0.028}^{+0.034} $$	$- 0 . 548_{- 0.056}^{+ 0.070}$ $Mathematical equation: $ -0.548_{-0.056}^{+0.070} $$
S2	23.850 ± 0.022	−0.622 ± 0.043	$23 . 837_{- 0.024}^{+ 0.029}$ $Mathematical equation: $ 23.837_{-0.024}^{+0.029} $$	$0 . 333_{- 0.031}^{+ 0.042}$ $Mathematical equation: $ 0.333_{-0.031}^{+0.042} $$	$23 . 851_{- 0.023}^{+ 0.027}$ $Mathematical equation: $ 23.851_{-0.023}^{+0.027} $$	$- 0 . 448_{- 0.047}^{+ 0.057}$ $Mathematical equation: $ -0.448_{-0.047}^{+0.057} $$
S4	23.821 ± 0.032	−0.511 ± 0.069	$23 . 806_{- 0.030}^{+ 0.038}$ $Mathematical equation: $ 23.806_{-0.030}^{+0.038} $$	$0 . 257_{- 0.040}^{+ 0.055}$ $Mathematical equation: $ 0.257_{-0.040}^{+0.055} $$	$23 . 816_{- 0.031}^{+ 0.037}$ $Mathematical equation: $ 23.816_{-0.031}^{+0.037} $$	$- 0 . 571_{- 0.064}^{+ 0.079}$ $Mathematical equation: $ -0.571_{-0.064}^{+0.079} $$
S5	23.847 ± 0.021	−0.618 ± 0.038	$23 . 831_{- 0.022}^{+ 0.027}$ $Mathematical equation: $ 23.831_{-0.022}^{+0.027} $$	$0 . 327_{- 0.028}^{+ 0.036}$ $Mathematical equation: $ 0.327_{-0.028}^{+0.036} $$	$23 . 846_{- 0.021}^{+ 0.025}$ $Mathematical equation: $ 23.846_{-0.021}^{+0.025} $$	$- 0 . 455_{- 0.041}^{+ 0.049}$ $Mathematical equation: $ -0.455_{-0.041}^{+0.049} $$

S367	23.834 ± 0.023	−0.609 ± 0.069	$23 . 828_{- 0.022}^{+ 0.027}$ $Mathematical equation: $ 23.828_{-0.022}^{+0.027} $$	$0 . 335_{- 0.045}^{+ 0.059}$ $Mathematical equation: $ 0.335_{-0.045}^{+0.059} $$	$23 . 833_{- 0.022}^{+ 0.026}$ $Mathematical equation: $ 23.833_{-0.022}^{+0.026} $$	$- 0 . 465_{- 0.067}^{+ 0.083}$ $Mathematical equation: $ -0.465_{-0.067}^{+0.083} $$
N147	23.781 ± 0.031	−0.436 ± 0.111	$23 . 775_{- 0.028}^{+ 0.035}$ $Mathematical equation: $ 23.775_{-0.028}^{+0.035} $$	$0 . 227_{- 0.060}^{+ 0.078}$ $Mathematical equation: $ 0.227_{-0.060}^{+0.078} $$	$23 . 778_{- 0.029}^{+ 0.034}$ $Mathematical equation: $ 23.778_{-0.029}^{+0.034} $$	$- 0 . 637_{- 0.092}^{+ 0.114}$ $Mathematical equation: $ -0.637_{-0.092}^{+0.114} $$
N235	23.830 ± 0.036	−0.654 ± 0.076	$23 . 830_{- 0.038}^{+ 0.050}$ $Mathematical equation: $ 23.830_{-0.038}^{+0.050} $$	$0 . 376_{- 0.056}^{+ 0.084}$ $Mathematical equation: $ 0.376_{-0.056}^{+0.084} $$	$23 . 838_{- 0.037}^{+ 0.046}$ $Mathematical equation: $ 23.838_{-0.037}^{+0.046} $$	$- 0 . 397_{- 0.083}^{+ 0.111}$ $Mathematical equation: $ -0.397_{-0.083}^{+0.111} $$
N6	23.865 ± 0.042	−0.652 ± 0.103	$23 . 862_{- 0.040}^{+ 0.055}$ $Mathematical equation: $ 23.862_{-0.040}^{+0.055} $$	$0 . 370_{- 0.068}^{+ 0.103}$ $Mathematical equation: $ 0.370_{-0.068}^{+0.103} $$	$23 . 868_{- 0.042}^{+ 0.051}$ $Mathematical equation: $ 23.868_{-0.042}^{+0.051} $$	$- 0 . 412_{- 0.103}^{+ 0.140}$ $Mathematical equation: $ -0.412_{-0.103}^{+0.140} $$

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