KiDS plus 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 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 ACDM 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 ACDM 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(DE)(a) = 1- Omega(m)(a), we find for the proportionality coefficients (alpha) over capB = 0.20(-0.33)(+0.20) and (alpha) over cap (M) = 0.25(-0.29)(+0.19). Our value of S-8 equivalent to sigma(8) root Omega(m)/0.3 is in better agreement with the Planck estimate when measured in the enlarged Horndeski parameter space than in a pure ACDM scenario. In our joint three-probe analysis, we report a downward shift of the S-8 best-fitting value from the Planck measurement of Delta S-8 = 0.0161:,7,44(8, in Horndeski gravity, compared to Delta S-8 = 0.0591:,14,(,' 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 r.inultiprobe analysis in both Lambda CDM and Horndeski gravity is publicly available athitps://github.com/alessiospuriomancini/KiDSHorndeski.