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Fig. 7.

Fig. 7. Refer to the following caption and surrounding text.

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Constraints on the effective Newtonian coupling μ (left) and the lensing modification ΣL, ∞ (right) as a function of scale factor in the small-scale limit, k → ∞, inferred from the combination of KiDS-Legacy, DESI DR2 BAO, eBOSS DR16 RSD, and Planck 2018 TTTEEE, low- TT, and low- EE datasets. The blue contour results from the analysis with Horndeski gravity modelled by the stable parameter basis D ̂ kin Mathematical equation: $ \hat{D}_{\mathrm{kin}} $ and Δ M ̂ 2 Mathematical equation: $ \Delta \hat{M}_*^2 $ and the green contour is inferred by sampling D ̂ kin Mathematical equation: $ \hat{D}_{\mathrm{kin}} $ and c ̂ s 2 Mathematical equation: $ \hat{c}_{\mathrm{s}}^2 $, while the orange contour corresponds to a direct sampling of α ̂ B Mathematical equation: $ \hat{\alpha}_{\mathrm{B}} $ and α ̂ M Mathematical equation: $ \hat{\alpha}_{\mathrm{M}} $ with αB(a) and αM(a) proportional to the dark energy density, following Eq. (6). The dashed lines show the GR values of μ = ΣL = 1. The solid line shows the mean of the posterior and the shaded region illustrates the 68% credible interval.

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