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 ( KiDS ) and the Galaxy And Mass Assembly ( GAMA ) survey .
The Horndeski class of dark energy/modified gravity models includes the majority of universally coupled extensions to \Lambda CDM 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 \Lambda CDM 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 \alpha _ { B } and \alpha _ { M } ( kinetic braiding and the Planck mass run rate , respectively ) to the dark energy density fraction \Omega _ { \mathrm { DE } } ( a ) = 1 - \Omega _ { \mathrm { m } } ( a ) , we find for the proportionality coefficients \hat { \alpha } _ { B } = 0.20 _ { -0.33 } ^ { +0.20 } and \hat { \alpha } _ { 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 \Lambda CDM scenario .
In our joint three-probe analysis we report a downward shift of the S _ { 8 } best fit 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 \Lambda CDM .
Our constraints are robust to the modelling uncertainty of the non-linear matter power spectrum in Horndeski gravity .
Our likelihood code for multi-probe analysis in both \Lambda CDM and Horndeski gravity is publicly available at \url https : //github.com/alessiospuriomancini/KiDSHorndeski .