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

¹ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing, 44780, Bochum, Germany
² Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121, Bonn, Germany
³ Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, I-00146, Rome, Italy
⁴ Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom
⁵ The Oskar Klein Centre, Department of Physics, Stockholm University, AlbaNova University Centre, SE-106 91, Stockholm, Sweden
⁶ Imperial Centre for Inference and Cosmology (ICIC), Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, United Kingdom
⁷ Department of Physics, Royal Holloway, University of London, Egham, TW20 0EX, United Kingdom
⁸ School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, NE1 7RU, Newcastle-upon-Tyne, United Kingdom
⁹ Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668, Warsaw, Poland
¹⁰ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193, Bellaterra (Barcelona), Spain
¹¹ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, United Kingdom
¹² Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense 40, E-28040, Madrid, Spain
¹³ Institute of Cosmology & Gravitation, Dennis Sciama Building, University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom
¹⁴ Leiden Observatory, Leiden University, P.O.Box 9513, 2300RA, Leiden, The Netherlands
¹⁵ Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, 94305, USA
¹⁶ SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
¹⁷ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020, Innsbruck, Austria
¹⁸ Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, United Kingdom
¹⁹ Donostia International Physics Center, Manuel Lardizabal Ibilbidea, 4, 20018, Donostia, Gipuzkoa, Spain
²⁰ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, I-40129, Bologna, Italy
²¹ Istituto Nazionale di Astrofisica (INAF) – Osservatorio di Astrofisica e Scienza dello Spazio (OAS), via Piero Gobetti 93/3, I-40129, Bologna, Italy
²² Istituto Nazionale di Fisica Nucleare (INFN) – Sezione di Bologna, viale Berti Pichat 6/2, I-40127, Bologna, Italy
²³ INAF – Osservatorio Astronomico di Padova, via dell’Osservatorio 5, 35122, Padova, Italy
²⁴ Institute for Particle Physics and Astrophysics, ETH Zürich, Wolfgang-Pauli-Strasse 27, 8093, Zürich, Switzerland
²⁵ Institute for Computational Cosmology, Ogden Centre for Fundamental Physics – West, Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom
²⁶ Centre for Extragalactic Astronomy, Ogden Centre for Fundamental Physics – West, Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom
²⁷ Graduate School of Science, Nagoya University, Furocho, Chikusa-ku, Nagoya, Aichi, 464-8602, Japan

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Received: 12 December 2025
Accepted: 16 February 2026

Abstract

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, ΔM_*² ≡ M_*² − 1, as model parameters, we constrained their present values as Δ M̂_∗² = 0.32^+0.07_−0.21 and D̂_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, S₈ = 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.