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

We present constraints on modified gravity from a cosmic shear analysis of the final data release of the Kilo-Degree Survey (KiDS-Legacy) in combination with DESI measurements of baryon acoustic oscillations, eBOSS observations of redshift space distortions, and cosmic microwave background (CMB) anisotropies from Planck. We studied the Horndeski class of modified gravity models in an effective field theory framework, employing a parametrisation that satisfies stability conditions by construction. In this work, for the first time, we present a cosmological analysis in this inherently stable parameter basis. Cosmic shear constrains the Horndeski parameter space significantly, matching or surpassing the CMB contribution. Adopting the de-mixed kinetic term of the scalar field perturbation, Dkin, and the deviation of the Planck mass from its fiducial value, ΔM*2 ≡ M*2 − 1, as model parameters, we constrained their present values as $ \Delta \hat{M}_*^2 = 0.32^{+0.07}_{-0.21} $ and $ \hat{D}_{\mathrm{kin}} = 3.74^{+0.69}_{-1.92} $, representing a deviation from general relativity (GR) at 1.5σ and 1.9σ, respectively. We derived constraints on the structure growth parameter, $ S_8 = 0.813^{+0.008}_{-0.011} $, which is compatible with the ΛCDM constraint at 0.54σ. We obtained the deviation of the effective Newtonian coupling from the GR value as Δμ∞, eff = 0.066 ± 0.023, corresponding to a 2.9σ significance. Although modified gravity provides a slightly better fit to the data, a model comparison only reveals a weak preference for modified gravity at the 1.4σ level. When adopting a dynamical dark energy model of the background cosmology, the inferred modified gravity parameter constraints are stable with respect to a the Λ cold dark matter (ΛCDM) cosmological background, while a mild preference at 1.57σ for dynamical dark energy remains.