  We consider theories containing scalar fields interacting with vector or with
tensor degrees of freedom, equipped with symmetries that prevent the
propagation of linearized scalar excitations around solutions of the equations
of motion. We first study the implications of such symmetries for building
vector theories that break Abelian gauge invariance without necessarily
exciting longitudinal scalar fluctuations in flat space. We then examine
scalar-tensor theories in curved space, and relate the symmetries we consider
with a non-linear realization of broken space-time symmetries acting on scalar
modes. We determine sufficient conditions on the space-time geometry to avoid
the propagation of scalar fluctuations. We analyze linearized perturbations
around spherically symmetric black holes, proving the absence of scalar
excitations, and pointing out modifications in the dynamics of spin-2
fluctuations with respect to Einstein gravity. We then study consequences of
this set-up for the dark energy problem, determining scalar constraints on
cosmological configurations that can lead to self-accelerating universes whose
expansion is insensitive to the value of the bare cosmological constant.
