  General Relativity extended through a dynamical scalar quartet is proposed as
a theory of the scalar-vector-tensor gravity, generically describing the
unified gravitational dark matter (DM) and dark energy (DE). The implementation
in the weak-field limit of the Higgs mechanism for the gravity, with a
redefinition of metric field, is exposed in a generally covariant form. Under a
natural restriction on parameters, the redefined theory possesses in the
linearized approximation by a residual transverse-diffeomorphism invariance,
and consistently comprises the massless tensor graviton and a massive scalar
one as a DM particle. A number of the adjustable parameters in the full
nonlinear theory and a partial decoupling of the latter from its weak-field
limit noticeably extend the perspectives for the unified description of the
gravity DM and DE in the various phenomena at the different scales.
