Evidence for dynamical dark energy with an evolving Hubble constant

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Table A.1.

‘D+P’, ‘D+D’, and ‘D+U’ represents the data combinations of DESI + Pantheon, DESI + DESY5, and DESI + Union, respectively. ‘M’, ‘G’, and ‘U’ represent the cases that the priors of w(z) are derived using the Matérn-3/2 kernel, the Gaussian kernels, and the Horndeski theory. ln(E) denotes the Bayesian evidence corresponding to each case.

Posterior distributions in 68% credible intervals for multi cases

Datasets	Cases	H₀(z ∼ 0.01)	H₀(z ∼ 2.35)	w(z ∼ 0.01)	w(z ∼ 0.62)	w(z ∼ 1.02)	w(z ∼ 1.52)	w(z ∼ 2.35)	Ω_m	Ω_bh²	ln(E)
		(km s⁻¹ Mpc⁻¹)
	M	$73 . 12_{- 0.85}^{+ 0.91}$ $Mathematical equation: $ 73.12^{+0.91}_{-0.85} $$	$71 . 46_{- 1.35}^{+ 1.31}$ $Mathematical equation: $ 71.46^{+1.31}_{-1.35} $$	$0 . 15_{- 1.16}^{+ 1.23}$ $Mathematical equation: $ 0.15^{+1.23}_{-1.16} $$	$- 1 . 20_{- 0.17}^{+ 0.17}$ $Mathematical equation: $ -1.20^{+0.17}_{-0.17} $$	$- 1 . 06_{- 0.15}^{+ 0.15}$ $Mathematical equation: $ -1.06^{+0.15}_{-0.15} $$	$- 0 . 88_{- 0.13}^{+ 0.13}$ $Mathematical equation: $ -0.88^{+0.13}_{-0.13} $$	$- 1 . 32_{- 0.25}^{+ 0.25}$ $Mathematical equation: $ -1.32^{+0.25}_{-0.25} $$	$0 . 35_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 0.35^{+0.02}_{-0.02} $$	$0 . 02193_{- 0.00050}^{+ 0.00053}$ $Mathematical equation: $ 0.02193^{+0.00053}_{-0.00050} $$	-744.96
	G	$73 . 11_{- 0.85}^{+ 0.90}$ $Mathematical equation: $ 73.11^{+0.90}_{-0.85} $$	$71 . 60_{- 1.26}^{+ 1.27}$ $Mathematical equation: $ 71.60^{+1.27}_{-1.26} $$	$0 . 29_{- 1.45}^{+ 1.61}$ $Mathematical equation: $ 0.29^{+1.61}_{-1.45} $$	$- 1 . 20_{- 0.12}^{+ 0.12}$ $Mathematical equation: $ -1.20^{+0.12}_{-0.12} $$	$- 1 . 06_{- 0.10}^{+ 0.10}$ $Mathematical equation: $ -1.06^{+0.10}_{-0.10} $$	$- 0 . 86_{- 0.10}^{+ 0.10}$ $Mathematical equation: $ -0.86^{+0.10}_{-0.10} $$	$- 1 . 38_{- 0.24}^{+ 0.24}$ $Mathematical equation: $ -1.38^{+0.24}_{-0.24} $$	$0 . 35_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 0.35^{+0.02}_{-0.02} $$	$0 . 02191_{- 0.00051}^{+ 0.00051}$ $Mathematical equation: $ 0.02191^{+0.00051}_{-0.00051} $$	-745.40
D+P	H	$73 . 27_{- 0.88}^{+ 0.85}$ $Mathematical equation: $ 73.27^{+0.85}_{-0.88} $$	$70 . 78_{- 0.98}^{+ 0.95}$ $Mathematical equation: $ 70.78^{+0.95}_{-0.98} $$	$- 1 . 82_{- 0.69}^{+ 0.68}$ $Mathematical equation: $ -1.82^{+0.68}_{-0.69} $$	$- 1 . 39_{- 0.28}^{+ 0.29}$ $Mathematical equation: $ -1.39^{+0.29}_{-0.28} $$	$- 0 . 98_{- 0.24}^{+ 0.25}$ $Mathematical equation: $ -0.98^{+0.25}_{-0.24} $$	$- 0 . 90_{- 0.20}^{+ 0.21}$ $Mathematical equation: $ -0.90^{+0.21}_{-0.20} $$	$- 1 . 25_{- 0.26}^{+ 0.26}$ $Mathematical equation: $ -1.25^{+0.26}_{-0.26} $$	$0 . 34_{- 0.02}^{+ 0.02}$ $Mathematical equation: $ 0.34^{+0.02}_{-0.02} $$	$0 . 02193_{- 0.00052}^{+ 0.00054}$ $Mathematical equation: $ 0.02193^{+0.00054}_{-0.00052} $$	-744.11
	wCDM	$72 . 18_{- 0.79}^{+ 0.77}$ $Mathematical equation: $ 72.18^{+0.77}_{-0.79} $$	−	$- 0 . 96_{- 0.03}^{+ 0.03}$ $Mathematical equation: $ -0.96^{+0.03}_{-0.03} $$	−	−	−	−	$0 . 30_{- 0.01}^{+ 0.01}$ $Mathematical equation: $ 0.30^{+0.01}_{-0.01} $$	$0 . 02246_{- 0.00058}^{+ 0.00053}$ $Mathematical equation: $ 0.02246^{+0.00053}_{-0.00058} $$	-749.14
	ΛCDM	$72 . 77_{- 0.55}^{+ 0.54}$ $Mathematical equation: $ 72.77^{+0.54}_{-0.55} $$	−	−	−	−	−	−	$0 . 31_{- 0.01}^{+ 0.01}$ $Mathematical equation: $ 0.31^{+0.01}_{-0.01} $$	$0 . 02228_{- 0.00056}^{+ 0.00055}$ $Mathematical equation: $ 0.02228^{+0.00055}_{-0.00056} $$	-745.65

	M	$71 . 33_{- 2.61}^{+ 2.59}$ $Mathematical equation: $ 71.33^{+2.59}_{-2.61} $$	$69 . 53_{- 1.38}^{+ 1.48}$ $Mathematical equation: $ 69.53^{+1.48}_{-1.38} $$	$0 . 08_{- 1.11}^{+ 1.36}$ $Mathematical equation: $ 0.08^{+1.36}_{-1.11} $$	$- 1 . 17_{- 0.17}^{+ 0.18}$ $Mathematical equation: $ -1.17^{+0.18}_{-0.17} $$	$- 0 . 85_{- 0.15}^{+ 0.15}$ $Mathematical equation: $ -0.85^{+0.15}_{-0.15} $$	$- 1 . 02_{- 0.14}^{+ 0.14}$ $Mathematical equation: $ -1.02^{+0.14}_{-0.14} $$	$- 1 . 82_{- 0.32}^{+ 0.30}$ $Mathematical equation: $ -1.82^{+0.30}_{-0.32} $$	$0 . 37_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 0.37^{+0.04}_{-0.04} $$	$0 . 02198_{- 0.00051}^{+ 0.00050}$ $Mathematical equation: $ 0.02198^{+0.00050}_{-0.00051} $$	-840.89
	G	$71 . 62_{- 2.58}^{+ 2.54}$ $Mathematical equation: $ 71.62^{+2.54}_{-2.58} $$	$69 . 59_{- 1.35}^{+ 1.47}$ $Mathematical equation: $ 69.59^{+1.47}_{-1.35} $$	$0 . 55_{- 1.44}^{+ 1.41}$ $Mathematical equation: $ 0.55^{+1.41}_{-1.44} $$	$- 1 . 14_{- 0.12}^{+ 0.14}$ $Mathematical equation: $ -1.14^{+0.14}_{-0.12} $$	$- 0 . 84_{- 0.11}^{+ 0.11}$ $Mathematical equation: $ -0.84^{+0.11}_{-0.11} $$	$- 1 . 00_{- 0.11}^{+ 0.11}$ $Mathematical equation: $ -1.00^{+0.11}_{-0.11} $$	$- 1 . 93_{- 0.33}^{+ 0.32}$ $Mathematical equation: $ -1.93^{+0.32}_{-0.33} $$	$0 . 37_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 0.37^{+0.04}_{-0.04} $$	$0 . 02196_{- 0.00050}^{+ 0.00052}$ $Mathematical equation: $ 0.02196^{+0.00052}_{-0.00050} $$	-841.32
D+D	H	$75 . 81_{- 3.39}^{+ 2.53}$ $Mathematical equation: $ 75.81^{+2.53}_{-3.39} $$	$67 . 41_{- 1.13}^{+ 1.36}$ $Mathematical equation: $ 67.41^{+1.36}_{-1.13} $$	$- 2 . 28_{- 0.92}^{+ 0.84}$ $Mathematical equation: $ -2.28^{+0.84}_{-0.92} $$	$- 1 . 36_{- 0.30}^{+ 0.32}$ $Mathematical equation: $ -1.36^{+0.32}_{-0.30} $$	$- 0 . 64_{- 0.27}^{+ 0.26}$ $Mathematical equation: $ -0.64^{+0.26}_{-0.27} $$	$- 0 . 94_{- 0.25}^{+ 0.25}$ $Mathematical equation: $ -0.94^{+0.25}_{-0.25} $$	$- 1 . 85_{- 0.35}^{+ 0.36}$ $Mathematical equation: $ -1.85^{+0.36}_{-0.35} $$	$0 . 43_{- 0.05}^{+ 0.04}$ $Mathematical equation: $ 0.43^{+0.04}_{-0.05} $$	$0 . 02196_{- 0.00051}^{+ 0.00051}$ $Mathematical equation: $ 0.02196^{+0.00051}_{-0.00051} $$	-840.03
	wCDM	$68 . 42_{- 1.23}^{+ 1.21}$ $Mathematical equation: $ 68.42^{+1.21}_{-1.23} $$	−	$- 0 . 84_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ -0.84^{+0.04}_{-0.04} $$	−	−	−	−	$0 . 30_{- 0.01}^{+ 0.01}$ $Mathematical equation: $ 0.30^{+0.01}_{-0.01} $$	$0 . 02196_{- 0.00063}^{+ 0.00063}$ $Mathematical equation: $ 0.02196^{+0.00063}_{-0.00063} $$	-844.28
	ΛCDM	$72 . 24_{- 0.66}^{+ 0.66}$ $Mathematical equation: $ 72.24^{+0.66}_{-0.66} $$	−	−	−	−	−	−	$0 . 32_{- 0.01}^{+ 0.01}$ $Mathematical equation: $ 0.32^{+0.01}_{-0.01} $$	$0 . 02195_{- 0.00059}^{+ 0.00060}$ $Mathematical equation: $ 0.02195^{+0.00060}_{-0.00059} $$	-848.55

	M	$74 . 05_{- 2.82}^{+ 2.80}$ $Mathematical equation: $ 74.05^{+2.80}_{-2.82} $$	$71 . 36_{- 2.01}^{+ 2.03}$ $Mathematical equation: $ 71.36^{+2.03}_{-2.01} $$	$0 . 33_{- 1.55}^{+ 1.54}$ $Mathematical equation: $ 0.33^{+1.54}_{-1.55} $$	$- 1 . 78_{- 0.40}^{+ 0.41}$ $Mathematical equation: $ -1.78^{+0.41}_{-0.40} $$	$- 0 . 31_{- 0.36}^{+ 0.36}$ $Mathematical equation: $ -0.31^{+0.36}_{-0.36} $$	$- 1 . 68_{- 0.34}^{+ 0.35}$ $Mathematical equation: $ -1.68^{+0.35}_{-0.34} $$	$- 0 . 59_{- 0.76}^{+ 0.78}$ $Mathematical equation: $ -0.59^{+0.78}_{-0.76} $$	$0 . 36_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 0.36^{+0.04}_{-0.04} $$	$0 . 02197_{- 0.00050}^{+ 0.00051}$ $Mathematical equation: $ 0.02197^{+0.00051}_{-0.00050} $$	-24.68
	G	$76 . 29_{- 3.35}^{+ 3.38}$ $Mathematical equation: $ 76.29^{+3.38}_{-3.35} $$	$71 . 79_{- 2.42}^{+ 2.52}$ $Mathematical equation: $ 71.79^{+2.52}_{-2.42} $$	$- 0 . 29_{- 2.00}^{+ 1.93}$ $Mathematical equation: $ -0.29^{+1.93}_{-2.00} $$	$- 2 . 39_{- 0.78}^{+ 0.80}$ $Mathematical equation: $ -2.39^{+0.80}_{-0.78} $$	$0 . 24_{- 0.62}^{+ 0.64}$ $Mathematical equation: $ 0.24^{+0.64}_{-0.62} $$	$- 2 . 06_{- 0.54}^{+ 0.52}$ $Mathematical equation: $ -2.06^{+0.52}_{-0.54} $$	$- 0 . 18_{- 1.35}^{+ 1.31}$ $Mathematical equation: $ -0.18^{+1.31}_{-1.35} $$	$0 . 37_{- 0.04}^{+ 0.04}$ $Mathematical equation: $ 0.37^{+0.04}_{-0.04} $$	$0 . 02196_{- 0.00053}^{+ 0.00052}$ $Mathematical equation: $ 0.02196^{+0.00052}_{-0.00053} $$	-24.91
D+U	H	$75 . 51_{- 3.51}^{+ 2.90}$ $Mathematical equation: $ 75.51^{+2.90}_{-3.51} $$	$68 . 38_{- 1.49}^{+ 1.75}$ $Mathematical equation: $ 68.38^{+1.75}_{-1.49} $$	$- 2 . 07_{- 0.94}^{+ 0.84}$ $Mathematical equation: $ -2.07^{+0.84}_{-0.94} $$	$- 1 . 60_{- 0.30}^{+ 0.30}$ $Mathematical equation: $ -1.60^{+0.30}_{-0.30} $$	$- 0 . 56_{- 0.27}^{+ 0.25}$ $Mathematical equation: $ -0.56^{+0.25}_{-0.27} $$	$- 1 . 40_{- 0.23}^{+ 0.24}$ $Mathematical equation: $ -1.40^{+0.24}_{-0.23} $$	$- 1 . 08_{- 0.42}^{+ 0.40}$ $Mathematical equation: $ -1.08^{+0.40}_{-0.42} $$	$0 . 41_{- 0.06}^{+ 0.05}$ $Mathematical equation: $ 0.41^{+0.05}_{-0.06} $$	$0 . 02199_{- 0.00051}^{+ 0.00050}$ $Mathematical equation: $ 0.02199^{+0.00050}_{-0.00051} $$	-23.75
	wCDM	$69 . 12_{- 1.47}^{+ 1.43}$ $Mathematical equation: $ 69.12^{+1.43}_{-1.47} $$	−	$- 0 . 86_{- 0.05}^{+ 0.05}$ $Mathematical equation: $ -0.86^{+0.05}_{-0.05} $$	−	−	−	−	$0 . 30_{- 0.01}^{+ 0.01}$ $Mathematical equation: $ 0.30^{+0.01}_{-0.01} $$	$0 . 02199_{- 0.00063}^{+ 0.00061}$ $Mathematical equation: $ 0.02199^{+0.00061}_{-0.00063} $$	-26.81
	ΛCDM	$72 . 32_{- 0.67}^{+ 0.66}$ $Mathematical equation: $ 72.32^{+0.66}_{-0.67} $$	−	−	−	−	−	−	$0 . 31_{- 0.01}^{+ 0.01}$ $Mathematical equation: $ 0.31^{+0.01}_{-0.01} $$	$0 . 02196_{- 0.00061}^{+ 0.00059}$ $Mathematical equation: $ 0.02196^{+0.00059}_{-0.00061} $$	-26.22

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