Vainshtein solutions without superluminal modes

The Vainshtein mechanism suppresses the fifth force at astrophysical distances, while enabling it to compete with gravity at cosmological scales. Typically, Vainshtein solutions exhibit superluminal perturbations. However, a restricted class of solutions with special boundary conditions was shown to be devoid of the faster-than-light modes. Here we extend this class by finding solutions in a theory of quasidilaton, amended by derivative terms consistent with its symmetries. Solutions with Minkowski asymptotics are not stable, while the ones that exhibit the Vainshtein mechanism by transitioning to cosmological backgrounds are free of ghosts, tachyons, gradient instability, and superluminality, for all propagating modes present in the theory. These solutions require a special choice of the strength and signs of nonlinear terms, as well as a choice of asymptotic cosmological boundary conditions.