Vainshtein mechanism in general purely disformal gravity theory

Abstract: We study a theory of gravity in which the action is a result from the general purely disformal transformation on the Einstein-Hilbert action. This theory is a sub-class of GLPV theory which is the the generalization of covariant Galileon. Nevertheless, we find that the self accelerating solution for the background universe disappears in this theory. We also find that, for this theory, the Vainshtein mechanism is absent. However, the Vainshtein mechanism is not necessary for this theory, because this theory can nearly mimic the Einstein theory of gravity at all scales inside the Huble radius without this mechanism.