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Publikace ÚTF

Covariant conserved currents for scalar-tensor Horndeski theory

Schmidt, J. and Bičák, J.

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.
journal:Journal of Mathematical Physics
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