KiDS + GAMA: constraints on horndeski gravity from combined large-scale structure probes

We present constraints on Horndeski gravity from a combined analysis of cosmic shear, galaxy–galaxy lensing and galaxy clustering from $450\, \mathrm{deg}^2$ of the Kilo-Degree Survey and the Galaxy And Mass Assembly survey.The Horndeski class of dark energy/modified gravity models includes the majority of universally coupled extensions to ΛCDM with one scalar field in addition to the metric. We study the functions of time that fully describe the evolution of linear perturbations in Horndeski gravity. Our results are compatible throughout with a ΛCDM model. By imposing gravitational wave constraints, we fix the tensor speed excess to zero and consider a subset of models including, e.g. quintessence and f(R) theories. Assuming proportionality of the Horndeski functions αB and αM (kinetic braiding and the Planck mass run rate, respectively) to the dark energy density fraction ΩDE(a) = 1 − Ωm(a), we find for the proportionality coefficients $\hat{\alpha }_\mathrm{ B} = 0.20_{-0.33}^{+0.20} \,$ and $\, \hat{\alpha }_\mathrm{ M} = 0.25_{-0.29}^{+0.19}$. Our value of $S_8 \equiv \sigma _8 \sqrt{\Omega _{\mathrm{m}}/0.3}$ is in better agreement with the Planck estimate when measured in the enlarged Horndeski parameter space than in a pure ΛCDM scenario. In our joint three-probe analysis, we report a downward shift of the S8 best-fitting value from the Planck measurement of $\Delta S_8 = 0.016_{-0.046}^{+0.048}$ in Horndeski gravity, compared to $\Delta S_8 = 0.059_{-0.039}^{+0.040}$ in ΛCDM. Our constraints are robust to the modelling uncertainty of the non-linear matter power spectrum in Horndeski gravity. Our likelihood code for multiprobe analysis in both ΛCDM and Horndeski gravity is publicly available at https://github.com/alessiospuriomancini/KiDSHorndeski.