The effective field theory of dark energy diagnostic of linear Horndeski theories after GW170817 and GRB170817A

We summarise the effective field theory of dark energy construction to explore observable predictions of linear Horndeski theories. Based on \cite{Perenon:2016blf}, we review the diagnostic of these theories on the correlation of the large-scale structure phenomenological functions: the effective Newton constant, the light deflection parameter and the growth function of matter perturbations. We take this opportunity to discuss the evolution of the bounds the propagation speed of gravitational waves has undergone and use the most restrictive one to update the diagnostic.