The scalar-tensor theories have become popular recently in particular in connection

with attempts to explain present accelerated expansion of the universe, but they have

been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural

choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for

perturbations of spacetimes in standard general relativity, we extend these methods

to the general Horndeski theory and find the covariant conserved currents for all four

Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential

that leads to the covariantly conserved current in the Branse-Dicke theory.

with attempts to explain present accelerated expansion of the universe, but they have

been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural

choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for

perturbations of spacetimes in standard general relativity, we extend these methods

to the general Horndeski theory and find the covariant conserved currents for all four

Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential

that leads to the covariantly conserved current in the Branse-Dicke theory.

typ: | article |
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journal: | Journal of Mathematical Physics |

volume: | 59 |

pages: | 042501 |

year: | 2018 |