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, D kin , and the deviation of the Planck mass from its fiducial value, Δ M * 2 ≡ M * 2 − 1, as model parameters, we constrained their present values as Δ M ̂ ∗ 2 = 0.32 +0.07 −0.21 and D ̂ kin = 3.74 +0.69 −1.92 , representing a deviation from general relativity (GR) at 1.5 σ and 1.9 σ , 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 0.54 σ . We obtained the deviation of the effective Newtonian coupling from the GR value as Δ μ ∞, eff = 0.066 ± 0.023, corresponding to a 2.9 σ 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 1.4 σ 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 1.57 σ for dynamical dark energy remains.