Jointly fitting weak lensing, x-ray, and Sunyaev-Zel'dovich data to constrain scalar-tensor theories with clusters of galaxies

Degenerate higher-order scalar-tensor (DHOST) theories are considered the most general class of scalar-tensor theories with an additional scalar field. DHOST theories modify the laws of gravity even at galaxy clusters scale hence affecting the weak lensing, x-ray, and Sunyaev-Zel'dovich observables. We derive the theoretical expression for the lensing convergence κ and the pressure profile P of clusters in the framework of DHOST theories and quantify how much they deviate from their general relativity counterparts. We argue that combined measurements of κ, P, and of the electron number density ne can constrain both the cluster parameters and some effective parameters of the DHOST theory. We carry on a Fisher matrix forecasts analysis to investigate whether this is indeed the case considering different scenarios for the spatial resolution and errors on the measured quantities.