Accelerating Horndeski cosmologies screening the vacuum energy

In the context of Horndeski cosmologies, we consider a dynamical adjustment mechanism able to screen any value of the vacuum energy of the matter fields leading to a fixed de Sitter geometry. Thus, we present the most general scalar-tensor cosmological models without higher than second order derivatives in the field equation that have a fixed spatially flat de Sitter critical point for any kind of material content or vacuum energy. These models allow us to understand the current accelerated expansion of the universe as the result of the evolution towards the critical point when it is an attractor.