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Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants. (English) Zbl 1381.83111
Summary: For a large class of scalar-tensor-like gravity whose action contains nonminimal couplings between a scalar field \(\phi (x^\alpha )\) and generic curvature invariants \(\left\{ {\mathcal {R}}\right\} \) beyond the Ricci scalar \(R=R^\alpha _{\;\;\alpha }\), we prove the covariant invariance of its field equation and confirm/prove the local energy-momentum conservation. These \(\phi (x^\alpha )-{\mathcal {R}}\) coupling terms break the symmetry of diffeomorphism invariance under an active transformation, which implies that the solutions to the field equation should satisfy the consistency condition \({\mathcal {R}}\equiv 0\) when \(\phi (x^\alpha )\) is nondynamical and massless. Following this fact and based on the accelerated expansion of the observable Universe, we propose a primary test to check the viability of the modified gravity to be an effective dark energy, and a simplest example passing the test is the “Weyl/conformal dark energy”.
MSC:
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C40 Gravitational energy and conservation laws; groups of motions
53Z05 Applications of differential geometry to physics
85A40 Cosmology
Software:
CosmoMC; NP; NPspinor
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