Abstract
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.
Highlights
The masslessness of the tensor graviton is safely ensured in general relativity (GR) by the conventionally adopted general gauge invariance/relativity
To ensure the generic property of the tensor masslessness it would suffice for a gravity theory to possess the invariance just under the volume-preserving/transverse diffeomorphisms (TDiff’s) [2]
A theory of gravity based on the explicit GR violation, with the residual TDiff invariance and an extra scalar mode contained in metric, was proposed in the non-generally covariant (GC) form in [3,4,5] and further elaborated in [6]
Summary
The masslessness of the tensor graviton is safely ensured in GR by the conventionally adopted general gauge invariance/relativity. To the minimal case, to maintain GC under the explicit GR violation it is necessary to introduce a nondynamical affine connection expressed minimally through a quartet of the scalar fields Such a proliferation of the uncontrollable nondynamical quantities in a semi-dynamical model makes one uneasy, both phenomenologically and theoretically, and may result in some conceptual problems. The linearized approximation (LA) for the most general version of the theory, as well as for its natural reduction insuring TDiff invariance, is considered The latter case, being unitary and free of ghosts and the classical instabilities, is argued to consistently comprise the massless tensor graviton and a massive scalar one as a DM particle. The nearest and far-away prospects for QMG are shortly discussed in Conclusion
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