KiDS-Legacy: Constraints on Horndeski gravity from weak lensing combined with galaxy clustering and cosmic microwave background anisotropies

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Table B.1.

Fit parameters for the combination of KiDS-Legacy, DESI DR2 BAO, eBOSS DR16 RSD, Planck 2018 TTTEEE, low-ℓ TT, and low-ℓ EE datasets with a fixed value of the lensing anomaly parameter, A_L = 1.

Model	S₈	Ω_m	χ_bestfit²	PTE	Δχ_bestfit²	N_σ
ΛCDM	$0 . 812_{- 0.008}^{+ 0.007}$ $Mathematical equation: $ 0.812^{+0.007}_{-0.008} $$	$0 . 300_{- 0.004}^{+ 0.003}$ $Mathematical equation: $ 0.300^{+0.003}_{-0.004} $$	1161.16	0.66	—	—
MG: ${\hat{D}}_{kin}$ $Mathematical equation: $ \hat{D}_{\mathrm{kin}} $$ , $Δ {\hat{M}}_{}^{2}$ $Mathematical equation: $ \Delta \hat{M}_^2 $$	$0 . 817_{- 0.009}^{+ 0.009}$ $Mathematical equation: $ 0.817^{+0.009}_{-0.009} $$	$0 . 298_{- 0.004}^{+ 0.003}$ $Mathematical equation: $ 0.298^{+0.003}_{-0.004} $$	1155.91	0.67	−5.25	1.80
MG: ${\hat{D}}_{kin}$ $Mathematical equation: $ \hat{D}_{\mathrm{kin}} $$ , ${\hat{c}}_{s}^{2}$ $Mathematical equation: $ \hat{c}_{\mathrm{s}}^2 $$	$0 . 811_{- 0.008}^{+ 0.009}$ $Mathematical equation: $ 0.811^{+0.009}_{-0.008} $$	$0 . 298_{- 0.003}^{+ 0.004}$ $Mathematical equation: $ 0.298^{+0.004}_{-0.003} $$	1153.25	0.67	−7.92	1.67
MG: ${\hat{α}}_{B}$ $Mathematical equation: $ \hat{\alpha}_{\mathrm{B}} $$ , ${\hat{α}}_{M}$ $Mathematical equation: $ \hat{\alpha}_{\mathrm{M}} $$	$0 . 827_{- 0.013}^{+ 0.014}$ $Mathematical equation: $ 0.827^{+0.014}_{-0.013} $$	$0 . 297_{- 0.003}^{+ 0.004}$ $Mathematical equation: $ 0.297^{+0.004}_{-0.003} $$	1152.85	0.68	−8.31	1.84

Notes. We report the marginal mode and 68% HPDI for S₈ and Ω_m, the best-fit χ² of our cosmological model, the model probability to exceed (PTE), the difference in χ² between ΛCDM and modified gravity models, and the N_σ preference level for modified gravity inferred in a Bayesian suspiciousness test.

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