Quartet-metric general relativity: scalar graviton, dark matter, and dark energy

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 extended gravity, with a redefinition of metric field, is exposed in a generally covariant form. Under a natural restriction on the parameters, the redefined theory possesses in the linearized approximation a residual transverse-diffeomorphism invariance, and consistently comprises the massless tensor graviton and a massive scalar one as a DM particle. The number of 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.